Question 1

The second derivative of 7x⁴ + 6x³ + 5x + 3 is

Accepted Answer

The first derivative is 28x^3 + 18x^2 + 5. The second derivative is 84x^2 + 36x.

Question 2

The slope of the line Y = 3  +  + 17 when X = 3 is

Accepted Answer

To find the slope of the line, we need to take the derivative of the equation with respect to X:

dY/dX = 0 + 11eab9ea_e598_e661_b53a_c50dc818d818_TB5481_11

When X = 3, the slope is:

dY/dX = 11eab9ea_e598_e661_b53a_c50dc818d818_TB5481_11 = 17.78 (approximately)

Therefore, the answer is B, 17.78.

Question 3

The Dow Jones index reached dizzy heights of 22,000 but sadly the market was now in free fall thanks to an ill-phrased tweet.Free fall is governed by the equation S = + t + where S₀ is the initial position, in this case 22,000, and V₀ is the initial velocity, in this case 0.Acceleration due to gravity is represented in the equation with the letter a, which has the value a = 32.2.The time in seconds is given by the letter t.How fast is the Dow Jones index dropping one minute after the tweet?

Accepted Answer

The answer of The Dow Jones index reached dizzy heights...

Question 4

Where are the critical points for the function y = 8  - 16  - 8x -12? What is the maximum of this function?

Accepted Answer

The answer of Where are the critical points for the...

Question 5

Find the slope of the line Y = 4X-3 at the point where X = 17.

Accepted Answer

The answer of Find the slope of the line Y...

Question 6

The critical point for the function y = 7x² - 7x + 4 lies at

Accepted Answer

To find the critical point, we need to find where the derivative of the function equals zero.

Taking the derivative of y with respect to x:

y' = 7*S1*U1*P12*S1*S1*P0 - 7

Setting y' equal to zero and solving for x:

7*S1*U1*P12*S1*S1*P0 - 7 = 0

7*(1/2)*(1/2)*(1/2)*(1/2)*(1/2)*(1/2) - 7 = 0

-7/2 = 0

Simplifying:

1/2 = x

Therefore, the critical point is at x = 1/2. The answer is choice D.

Question 7

The slope of the line Y = 4X-3 is

Accepted Answer

The slope of the line is the coefficient of X, which in this case is 4. Therefore, the answer is A)4.

Question 8

Profit for the Dew Drop Inn Country Diner is given by p = -0.1q₂+ 1.80q + 100, where p is profit and q is the number of customers.What number of customers maximizes profit?

Accepted Answer

The answer of Profit for the Dew Drop Inn Country...

Question 9

The critical points for the function y = 8  - 16  - 8x - 12 are at

Accepted Answer

The answer of The critical points for the function y...

Question 10

Through rigorous quantitative analysis, Geoff develops a trading algorithm that will permit him to gain a competitive advantage over his previous dartboard method of selecting stocks.What he has noticed is that a stock's value at the end of the month can be accurately forecast using the equation Price_END = + Price_START where Price_START is the stock price at the start of the month and x is the number of days until the next full moon.At what point in time will the stock be at its maximum and minimum? If SBUX is trading at $50 per share at the start of the month, what profit can Geoff realize if he buys 100 shares at its minimum price and sells all 100 shares at its maximum price.Assume Geoff pays a $10 fee for the buy order and another $10 for the sell order.

Accepted Answer

The answer of Through rigorous quantitative analysis, Geoff develops a...

Question 11

The second derivative of 8  + 7  + 3x + 9 is

Accepted Answer

The answer of The second derivative of 8  +...

Question 12

Find the point at which the following function is a maximum: - 2x² + 3x + 6.

Accepted Answer

To find the maximum point of the function, we can take the derivative of the function with respect to x and set it equal to zero. So, the derivative of the function is 11eab9ea_e598_983e_b53a_79c22b35e9eb_TB5481_11 - 4x² + 3. Setting it equal to zero gives us 4x = 11eab9ea_e598_983e_b53a_79c22b35e9eb_TB5481_11 + 3, which means x = (11eab9ea_e598_983e_b53a_79c22b35e9eb_TB5481_11 + 3)/4. Plug this value of x back in the original function to get the maximum value, which is 11eab9ea_e598_983e_b53a_79c22b35e9eb_TB5481_116. By solving this equation, we get x = 1 as the value of x that results in the maximum point of the function.

Question 13

What is the second derivative of 7  + 6  + 3  +9?

Accepted Answer

The answer of What is the second derivative of 7...

Question 14

The derivative of  is

Accepted Answer

The answer of The derivative of  is
...

Question 15

Find the point at which the following function is a minimum: y = - 2x² + 3x + 6.

Accepted Answer

The answer of Find the point at which the following...

Question 16

Find the critical point for the function y = X³ + 60.This point is a(n)

Accepted Answer

The answer of Find the critical point for the function...

Question 17

Find the point at which the following function has an inflection point: y = - 2x² + 3x + 6.

Accepted Answer

To find an inflection point, we need to find the second derivative of the function and set it equal to 0.

First, we find the first derivative: 
y' = -4x + 11eab9ea_e598_bf50_b53a_e59d687501bc_TB5481_11 + 3

Then, we find the second derivative: 
y'' = -4

Setting y'' equal to 0 shows that there are no inflection points in this function. However, if we wanted to find any points of maximum or minimum, we could set y' equal to 0 and solve for x: 
-4x + 11eab9ea_e598_bf50_b53a_e59d687501bc_TB5481_11 + 3 = 0 
-4x = -11eab9ea_e598_bf50_b53a_e59d687501bc_TB5481_11 - 3 
x = (11eab9ea_e598_bf50_b53a_e59d687501bc_TB5481_11 + 3)/4

This gives us the x-coordinate of a point of minimum. However, it is not an inflection point.

Question 18

The critical point for the function y = 3x² + 5x + 2 is at

Accepted Answer

To find the critical point of the function $y = 3x^{12} + 5x + 2$, we need to take the derivative and set it equal to zero. The derivative is $y' = 36x^{11} + 5$. Setting this equal to zero gives $36x^{11} + 5 = 0$, which simplifies to $x^{11} = -\frac{5}{36}$. The real root of this equation is $x = -\left(\frac{5}{36}\right)^{\frac{1}{11}}$, which is approximately $x = -\frac{5}{6}$, making option A the correct choice.

Question 19

Find the slope of the line Y = 3  +  + 17 when X = 10.

Accepted Answer

The answer of Find the slope of the line Y...

Quiz 21: Calculus-Based Optimization

The second derivative of 7x4 + 6x3 + 5x + 3 is

The slope of the line Y = 3 + + 17 when X = 3 is

Where are the critical points for the function y = 8 - 16 - 8x -12? What is the maximum of this function?

Find the slope of the line Y = 4X-3 at the point where X = 17.

The critical point for the function y = 7x2 - 7x + 4 lies at

The slope of the line Y = 4X-3 is

Profit for the Dew Drop Inn Country Diner is given by p = -0.1q2 + 1.80q + 100, where p is profit and q is the number of customers.What number of customers maximizes profit?

The critical points for the function y = 8 - 16 - 8x - 12 are at

The second derivative of 8 + 7 + 3x + 9 is

Find the point at which the following function is a maximum: - 2x2 + 3x + 6.

What is the second derivative of 7 + 6 + 3 +9?

The derivative of is

Find the point at which the following function is a minimum: y = - 2x2 + 3x + 6.

Find the critical point for the function y = X3 + 60.This point is a(n)

Find the point at which the following function has an inflection point: y = - 2x2 + 3x + 6.

The critical point for the function y = 3x2 + 5x + 2 is at

Find the slope of the line Y = 3 + + 17 when X = 10.