For y=f(x) = 3x^2, find Δx, Δy, and Δy/Δx' given x1 = 1 and x2 = 5

The number of random samples, obtained using the formula for combination are 230,300 random samples

A random sample is a subset of the population, such that each member of the subset have the same chance of being selected.

The formula for combinations indicates that we get;

nCr = n!/(r!*(n - r)!), where;

n = The size of the population

r = The sample size

The number of different simple random samples of size 4 that can be obtained from a population of size 50 therefore can be obtained using the above equation by plugging in r = 4, and n = 50, therefore, we get;

nCr = 50!/(4!*(50 - 4)!) = 230300

The number of different ways and therefore, the number of random samples of size 4 that can be selected from a population of 50 therefore is 230,300 random samples.

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The height of the rectangular frame is 30 inches.

Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. The rectangular frame's diagonal is 50 inches and forms a 36.87° angle with the bottom of the frame.

Hence, the height of the frame can be represented as follows:

using trigonometric ratios,

sin 36.87 = opposite / hypotenuse

sin 36.87 = h / 50

cross multiply

h = 50 sin 36.87

h = 50 × 0.60000142913

h = 30.0000714566

Therefore,

height of the frame = 30 inches

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To find the length of the ladder needed to reach the roof of the shed that is 35 ft from the ground with the base of the ladder 12 ft from the shed, you can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the ladder, in this case) is equal to the sum of the squares of the other two sides (the height and the distance from the shed).

Step 1: Identify the sides of the triangle.
- Height (a): 35 ft (vertical side)
- Distance from the shed (b): 12 ft (horizontal side)
- Ladder length (c): Hypotenuse

Step 2: Apply the Pythagorean theorem.
- a² + b² = c²
- 35² + 12² = c²

Step 3: Calculate the squares and sum them.
- (35 * 35) + (12 * 12) = c²
- 1225 + 144 = c²
- 1369 = c²

Step 4: Find the length of the ladder (c).
- c = √1369
- c = 37

The ladder needs to be 37 ft long to reach the roof of the shed.

Shortening the distance between the ladder and the shed will affect the height of the ladder by making it steeper. This will cause the ladder to be higher above the ground, but it may also make it less stable and more difficult to climb.

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We reflect the point (-5, -3) over the x-axis to get (-5, 3), and then translate this point down by 2 units to get the final coordinates of (-5, 1).

To reflect a point over the x-axis, we keep the x-coordinate the same, but negate the y-coordinate. Thus, reflecting the point (-5, -3) over the x-axis gives us the point (-5, 3).

Next, we need to translate the result 2 units down. To do this, we subtract 2 from the y-coordinate of the reflected point. So, subtracting 2 from the y-coordinate of (-5, 3) gives us the final coordinates:

(-5, 3) translated 2 units down is (-5, 1).

In summary, we can reflect a point over the x-axis by negating the y-coordinate, and translate a point down by subtracting a value from its y-coordinate. So, we reflect the point (-5, -3) over the x-axis to get (-5, 3), and then translate this point down by 2 units to get the final coordinates of (-5, 1).

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Booker bought 8 servings of almonds.

One serving of almonds is equal to 1/3 cup.

To find how many servings of almonds Booker bought, we can divide the total amount of almonds he purchased by the amount in one serving:

2 and 2/3 cups of almonds = 8/3 cups of almonds

Number of servings = (total amount of almonds purchased) / (amount in one serving)

Number of servings = (8/3) / (1/3)

Number of servings = 8/3 x 3/1

Number of servings = 8

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Using division operation with unit conversions, the length of ribbon that each of the 18 students in Mrs. Hinojosa's class gets is as follows:

a) 4.2 feet.

b) 4 feet and 2 inches

c) 50 inches.

Division and multiplication operations are used in unit conversions.

Unit conversions involve converting measurements from hours to minutes or seconds, centimeters to meters and miles, etc.

The total quantity of ribbon Mrs. Hinojosa had = 75 feet

1 foot = 12 inches

75 feet = 900 inches (75 x 12)

The number of students in the class = 18

The length of ribbon received by each student = 4.167 feet (75 ÷ 18)

The length of ribbon received by each student ≈ 4 feet and 2 inches

The length of ribbon received by each student in inches only = 50 inches (900 ÷ 18)

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We can use the Pythagorean theorem to relate the distances between the ladder, wall, and ground. Let's call the distance from the foot of the ladder to the wall "x", and the distance from the top of the ladder to the ground "y". Then, we know that:

x^2 + y^2 = 10^2

We can differentiate this equation with respect to time to get:

2x(dx/dt) + 2y(dy/dt) = 0

We're interested in finding dy/dt, the rate at which the top of the ladder is sliding down the wall. We know that dx/dt = 0.5 ft/s, so we can plug in these values and solve for dy/dt:

2x(dx/dt) + 2y(dy/dt) = 0
2(8)(0.5) + 2y(dy/dt) = 0 (since x = 8 based on the Pythagorean theorem)
dy/dt = -4 ft/s

So the top of the ladder is sliding down the wall at a rate of 4 ft/s.
When the 10-foot ladder is leaning against a vertical wall, it forms a right-angled triangle with the wall and the ground. As Jack pulls the foot of the ladder away from the wall at a rate of 0.5 ft/s, the top of the ladder slides down the wall. To find the rate at which the top of the ladder slides down, we can use the Pythagorean theorem:

a^2 + b^2 = c^2

where a is the distance from the foot of the ladder to the wall, b is the height of the ladder's top from the ground, and c is the length of the ladder (10 feet).

Differentiating both sides with respect to time (t), we get:

2a(da/dt) + 2b(db/dt) = 0

We know that da/dt = 0.5 ft/s. We need to find db/dt, which is the rate at which the top of the ladder slides down the wall. To do this, we need to find the values of a and b at a given moment. Since the problem doesn't provide this information, it's not possible to determine the exact value of db/dt. However, if you have the values of a and b, you can plug them into the equation and solve for db/dt.

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Thus, the area of triangle for the given values of height and base is found as:  180 sq. in.

A number of steps are involved in the Unit of Conversion process, which involves multiplying or dividing by a numerical factor. There are numerous ways to measure things like weight, separation, and temperature.

Unit conversion is the process of changing the unit of measurement for a comparable quantity by multiplying or dividing by conversion factors.

Scientific notation is used to express the units, which are then translated into numerical values in accordance with the amounts.

Given data:

We know that,

1 foot  = 12 in.

2 feet = 12*2 = 24 in.

Area of triangle = 1/2 * b * h

Area of triangle = 1/2 * 24 * 15

Area of triangle = 12* 15

Area of triangle = 180 sq. in

Thus, the area of triangle for the given values of height and base is found as:  180 sq. in.

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The image of ABC under the translation by 1 unit to the right and 4 units up is the triangle with vertices A', B', and C'.

A triangle is a closed two-dimensional geometric shape with three straight sides and three angles. It is one of the basic shapes in geometry and has been studied since ancient times. To translate a figure by a given vector, you need to move each point of the figure by the same amount and in the same direction as the vector. In this case, we want to translate ABC by a vector of (1, 4), which means we need to move each point of ABC one unit to the right and four units up.

Let's say the coordinates of the points of ABC are:

A = [tex]\rm (x_1, y_1)[/tex]

B = [tex]\rm (x_2, y_2)[/tex]

C = [tex]\rm (x_3, y_3)[/tex]

To translate ABC by the vector (1, 4), we add 1 to each x-coordinate and 4 to each y-coordinate:

A' = [tex]\rm (x_1 + 1, y_1 + 4)[/tex]   (x₁ + 1, y₁ + 4)

B' = [tex]\rm (x_2 + 1, y_2 + 4)[/tex]   (x₂ + 1, y₂ + 4)

[tex]\rm C' = (x_3 + 1, y_3 + 4)[/tex]  (x₃ + 1, y₃ + 4)

Therefore, The image of ABC under the translation by 1 unit to the right and 4 units up is the triangle with vertices A', B', and C'.

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Selika spends £565.85 on labour costs.

Given, Selika spends money on plants, materials, and labor in the ratio of 1:5:12 and spends a total of £848.75. We have to find how much money she spends on labor costs.

Let the amount of money Selika spends on plants be x. Then, the amount of money she spends on materials is 5x, and the amount of money she spends on labor is 12x.

The total amount of money she spends is £848. 75

x + 5x + 12x = 848.75

18x = 848.75

x = 848.75/18

x = 47.15

She spend on labour 12x = 12 × 47.15

= 565.85

Therefore, Selika spends £565.85 on labour costs.

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Answer:

Step-by-step explanation:

Let the three-digit number be represented as $abc$, where $a$ is the hundreds digit, $b$ is the tens digit, and $c$ is the units digit.

From the problem, we have two equations:

Equation 1: $2a=b+2$

Equation 2: $c=3a$

We can use these equations to solve for $a$, $b$, and $c$.

Starting with Equation 1, we can isolate $b$ to get $b=2a-2$.

Next, we can substitute Equation 2 into Equation 1 to get $2a=3a-6+2$, which simplifies to $a=8$.

Using this value of $a$, we can now find $b$ and $c$. From Equation 2, we have $c=3a=24$. And from Equation 1, we have $b=2a-2=14$.

Thus, the original three-digit number is $abc=824$.

When we reverse the digits to get $cba=428$, we increase the number by 594, so we have $cba=abc+594=824+594=1418$.

Therefore, the answer is $\boxed{824}$.

The set that includes ONLY rational numbers that are also integers is:

{-3, -2, -1, 0, 1, 2, 3, ...}

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Answer:

A

Step-by-step explanation:

Let's call the length of each of the other two sides x. Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as 6 + x + x Simplifying this equation, we get  2x + 6 We know that the perimeter is 22 cm so we can set up an equation and solve for x. 22 = 2x + 6 Subtracting 6 from both sides, we get  16 = 2x Dividing both sides by 2, we get x=8

The amount of energy the refrigerator uses per day is 3.6 kilowatt-hour (kWh)

The refrigerator energy usage per day in BTU is 12283.704 BTU

The BTU is an acronym for the British Thermal Unit, which is a measure of heat, which is specified in energy units.

The duration the refrigerator fan runs per hour = 30 minutes

The amount of energy the refrigerator uses every hour = 300 watts × 0.5 hour/hour = 150 watts

The amount of energy the refrigerator uses per hour = 150 watt-hour

1 kWh = 3412.14 BTU

Therefore;

The amount of energy in BTU the refrigerator uses per day = 12283.704 BTU

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The equation models the situation described in the problem is 3.50x + 2.25(10) = 3 (x + 10) . The correct answer is C.

To model the situation described in the problem, we need to use an equation that represents the total cost of the flowers in terms of the number of roses (x) and the number of carnations (10). Let's assume that the cost of each flower is proportional to its price, and that the average cost per flower is the total cost divided by the total number of flowers (x + 10).

The cost of x roses at $3.50 each is 3.50x, and the cost of 10 carnations at $2.25 each is 2.25(10) = 22.50. Therefore, the total cost of the bouquet is:

Total cost = 3.50x + 22.50

The average cost per flower is given by:

Average cost = Total cost / (x + 10)

We are told that the average cost per flower is $3.00, so we can set up an equation:

3.00 = (3.50x + 22.50) / (x + 10) or  3.50x + 2.25(10) = 3 (x + 10)

This equation models the situation described in the problem. We can solve for x to find the number of roses needed to make a bouquet that meets the given conditions. The correct answer is C.

Your question is incomplete but most probably your full question attached below

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Step 1: Answer

The point (2, 8) is the point (x1, y1) identified from the equation y - 8 = 3(x - 2).

Step 2: Explanation

The equation y - 8 = 3(x - 2) is in point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope of the line. In this case, the slope of the line is 3, which means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.

Comparing the given equation with the point-slope form, we can see that x1 = 2 and y1 = 8. Therefore, the point (2, 8) is the point identified from the equation.

Anallency will have $134.46 more money than Alejandro after one year of their respective deposits.

Alejandro and Anallency are depositing money in separate accounts with different interest rates. Alejandro is depositing $1,750 in an account that earns a simple interest rate of 6.5% per year, while Anallency is depositing $1,675 in an account that earns a compounded interest rate of 7.5% per year. After one year of their respective deposits, Anallency will have $134.46 more money than Alejandro.

The difference in interest earned between the two accounts is the reason for the difference in money earned by Alejandro and Anallency. Alejandro's account earns a simple interest rate, which means that he earns 6.5% of his initial deposit every year, regardless of how much interest he has already earned.

On the other hand, Anallency's account earns a compounded interest rate, which means that she earns interest on both her initial deposit and on any interest earned in previous years.

The formula for calculating simple interest is I = Prt, where I is the interest earned, P is the principal (or initial deposit), r is the interest rate, and t is the time in years. Using this formula, we can calculate that Alejandro will earn $113.75 in interest after one year.

The formula for calculating compounded interest is A = P(1 + r/n)^(nt), where A is the amount of money at the end of the time period, P is the principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Using this formula, we can calculate that Anallency will have $248.21 more in her account than Alejandro after one year.

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Answer: To find the length of the midsegment of a trapezoid, you need to add the lengths of the two bases together and divide by 2.

The length of the top base is 2n-2 and the length of the bottom base is 4n+6.

Adding the two bases together gives:

(2n-2) + (4n+6) = 6n + 4

Dividing by 2 gives:

(6n + 4) / 2 = 3n + 2

Therefore, the length of the midsegment of the trapezoid is 3n + 2.

Keep in mind that if Lourdes is able to pay off her credit card balance at the end of the month, she won't be charged any interest, making the credit card the better option in that case.

To determine whether Lourdes should use a debit card or credit card, we need to consider the ATM fee and the potential interest charges from the credit card.

Step 1: Determine the ATM fee
Find out how much Lourdes would be charged for using the ATM to withdraw cash.

Step 2: Determine the interest rate on the credit card
Check the credit card's terms and conditions to find the annual percentage rate (APR). This will help us calculate the potential interest charges.

Step 3: Calculate the potential interest charges
Assuming Lourdes doesn't pay off the credit card balance by the end of the month, divide the APR by 12 to get the monthly interest rate. Multiply this rate by the $48 grocery cost to find the potential interest charges.

Step 4: Compare costs
Compare the ATM fee and potential interest charges to determine the cheaper option. If the ATM fee is less than the potential interest charges, Lourdes should use her debit card. If the potential interest charges are less than the ATM fee, she should use her credit card.

Keep in mind that if Lourdes is able to pay off her credit card balance at the end of the month, she won't be charged any interest, making the credit card the better option in that case.

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The value of the velocity, u is 19.6 m/s.

The greatest height reached by the particle is 19.6 m.

The total time during which the particle is at a height greater than half its greatest height is 2.33 s.

a) To find the value of the velocity, u, we can use the formula for the time of flight of a vertically projected particle:

t = 2u/g

Since the particle returns to the same point after 4 seconds, we have:

2t = 4

Substituting the value of t in the first equation, we get:

u = gt/2 = 9.8 x 2

u = 19.6 m/s

b) To find the greatest height reached by the particle, we can use the formula for the maximum height reached by a vertically projected particle:

h = u^2/2g

Substituting the value of u, we get:

h = 19.6^2/(2 x 9.8)

h = 19.6 m

c) To find the total time during which the particle is at a height greater than half its greatest height, we can first find the height at which the particle is at half its greatest height:

h/2 = (u^2/2g)/2 = u^2/4g

Substituting the value of u, we get:

h/2 = 19.6^2/(4 x 9.8) = 24.01 m

So, the particle is at a height greater than half its greatest height when it is above 24.01 m.

Next, we can find the time taken by the particle to reach this height:

h = ut - (1/2)gt^2

24.01 = 19.6t - (1/2)9.8t^2

Solving this quadratic equation, we get:

t = 2.33 s or t = 4.10 s

The particle takes 2.33 s to reach a height of 24.01 m, and it takes another 1.67 s (4 - 2.33) to return to the ground.

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From the solution to the question that we have here, the answer is A. There is no solid proof that the number of hours worked dropped after the income rise.

Let μ be the population mean number of hours worked per week by teachers who work part-time jobs, after the salary increase. Here are the alternate and null hypotheses:

H0: μ = 13

H1: μ < 13

n = 400

[tex]\bar{X}=12.5[/tex]

μ = 13

Formula for the t-test statistics is

[tex]t = \frac{\bar{X}-\mu}{s/\sqrt{n} }[/tex]

t = (12.5 - 13)/(6.5/√400)

t = (- 0.5)/(6.5/20)

t = - 10/6.5

= -1.5388

Degree of freedom is 400 -1 = 399

α = 0.05

The p-value is p(t < -1.5385) = 0.062

The p-value exceeds the level of significance. Therefore, we unable to reject the null hypothesis.

Hence, option a is correct.

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The discount amount of the bike Sarah wants to buy is $60. The calculation was done by using the formula: Discount = Original price x Percent off.

To find the discount amount of the bike, we need to use the formula

Discount = Original Price x Discount Rate

where Discount Rate = Percent Off / 100

We know that the original price of the bike is $150 and it is now 40% off. So, the discount rate is

Discount Rate = 40 / 100 = 0.4

Substituting these values in the formula, we get:

Discount = $150 x 0.4 = $60

Therefore, the discount amount of the bike is $60.

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Answer:

Absoblute value Reflection

Step-by-step explanation:

You can tell it's absolbute value because of the parbolas, and it's reflected acroos the two points. Give brainliest please!

Marsha would save $26,040 over the life of the loan if she purchases the 3 points.

First, let's calculate the monthly payment if Marsha doesn't purchase any points. We can use a mortgage calculator or the PMT function in Excel to find;

PMT = $1,987.13

Now, let's calculate the monthly payment if Marsha purchases 3 points;

Loan amount = $350,000

Points cost = 3 points × 1% × $350,000 = $10,500

Effective loan amount = $350,000 - $10,500 = $339,500

Interest rate = 4.5% / 12 = 0.375%

Number of payments=20 years × 12 = 240

Using the PMT function, we get;

PMT = $1,878.63

So, by purchasing 3 points, Marsha can save;

$1,987.13 - $1,878.63 = $108.50 per month

Over the life of the loan, which is 20 years or 240 months, the total savings would be;

$108.50 × 240 = $26,040

Therefore, Marsha would save $26,040 amount of money.

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Therefore , the solution of the given problem of inequality comes out to be the solutions x = -6 or x = -10 would be acceptable.

Algebra, which lacking a symbol for this difference, can represent it using a pair or group of numbers. Equity usually comes after equilibrium. Inequality is bred by the persistent gap of standards. Equality and disparity are not the same thing. As was my least preferred symbol, notwithstanding knowing that the pieces are often not connected or close to one another. (). No matter how small the variations, they all affect value.

Here,

Finding values of x that cause the left side of the inequality to be bigger than the right side is necessary to make the inequality -2x > 10 true. Divide both sides by -2 and invert the inequality sign to achieve this:

=> -2x > 10

=> x < -5

The inequality is therefore true for any value of x that is less than -5. For instance, the solutions x = -6 or x = -10 would be acceptable.

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Number that produces a rational number when multiplied by 1 is option B, -3.

To determine which number produces a rational number when multiplied by 1,

We need to examine each of the given.

Here, options: A. TI , B. -3, C. T, D. -1.41421356

We know,

A rational number can be expressed as a fraction (a/b) where both a and b are integers and b is not equal to 0. When multiplying by 1, the result remains the same. Option B: -3 multiplied by 1 = -3 which is a rational number because it can be expressed as a fraction (-3/1).

Option D: here given number -1.41421356 multiplied by 1 = -1.41421356 and we cannot be easily expressed as a fraction.

Therefore,it's not a rational number.

Thus, the number that produces a rational number when multiplied by 1 is option B, -3.

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a. To find the probability that there are no cars in the system, we need to use the formula for the steady-state probability distribution of the M/M/1 queue:
P(0) = (1 - λ/μ)
where λ is the arrival rate (2 per hour) and μ is the service rate (3 per hour).
P(0) = (1 - 2/3) = 1/3 or 0.3333
Therefore, the probability that there are no cars in the system is 0.3333.

b. To find the average number of cars in the system, we can use Little's Law:
L = λW
where L is the average number of cars in the system, λ is the arrival rate (2 per hour), and W is the average time spent in the system.
We can solve for W by using the formula:
W = 1/(μ - λ)
W = 1/(3 - 2) = 1 hour
Therefore, the average number of cars in the system is:
L = λW = 2 x 1 = 2 cars

c. To find the average time spent in the system, we already calculated W in part b:
W = 1 hour

d. To find the probability that there are exactly two cars in the system, we need to use the formula for the steady-state probability distribution:
P(n) = P(0) * (λ/μ)^n / n!
where n is the number of cars in the system.
P(2) = P(0) * (λ/μ)^2 / 2!
P(2) = 0.3333 * (2/3)^2 / 2
P(2) = 0.1111 or 11.11%
Therefore, the probability that there are exactly two cars in the system is 11.11%.

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Since each of the bricks is the same exact size, then each brick is 0.6 meters tall.

To determine the height of each glowing brick, we need to divide the total height of the tower (5.4 meters) by the number of bricks (9). This gives us the average height of each brick.

Using the formula for division, we can write this as:

Height of each brick = Total height of tower / Number of bricks

Plugging in the given values, we get:

Height of each brick = 5.4 meters / 9 bricks

Simplifying this expression, we can cancel out the units of "bricks" to get:

Height of each brick = 0.6 meters

Therefore, each glowing brick in the tower is 0.6 meters tall.

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The critical points and their classifications are:

(0, 1) - saddle point

(0, -1) - saddle point

(6, 1) - local minimum

(6, -1) - local minimum

To find the critical points of the function f(x, y) = x³ + y³ – 9x² – 3y - 6, we need to find the points where the partial derivatives of f with respect to x and y are zero.

∂f/∂x = 3x² - 18x = 3x(x - 6)

∂f/∂y = 3y² - 3 = 3(y² - 1)

Setting these partial derivatives equal to zero and solving for x and y, we get:

x = 0 or x = 6

y = ±1

So the critical points are (0, 1), (0, -1), (6, 1), and (6, -1).

To classify each critical point, we need to compute the second partial derivatives of f:

∂²f/∂x² = 6x - 18

∂²f/∂y² = 6y

∂²f/∂x∂y = 0

At (0, 1):

∂²f/∂x² = -18 < 0 (concave down)

∂²f/∂y² = 6 > 0 (concave up)

So (0, 1) is a saddle point.

At (0, -1):

∂²f/∂x² = -18 < 0 (concave down)

∂²f/∂y² = 6 > 0 (concave up)

So (0, -1) is a saddle point.

At (6, 1):

∂²f/∂x² = 18 > 0 (concave up)

∂²f/∂y² = 6 > 0 (concave up)

So (6, 1) is a local minimum.

At (6, -1):

∂²f/∂x² = 18 > 0 (concave up)

∂²f/∂y² = 6 > 0 (concave up)

So (6, -1) is a local minimum.

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