Question 1

Suppose  . Then  has a local minimum value of 9 at the point (2, 3) when A = _____, B = _____, and C = _____.

Accepted Answer

The answer of Suppose  . Then  has a...

Question 2

Find the following partial derivative: f_xy if . A) B) C) D) E)

Accepted Answer

Applying the chain rule, we have:

$\frac{\partial f}{\partial S1} = \frac{\partial f}{\partial U1}\cdot\frac{\partial U1}{\partial S1}$

$\frac{\partial f}{\partial U1} = \frac{\partial f}{\partial B1}\cdot\frac{\partial B1}{\partial U1}$

$\frac{\partial f}{\partial B1} = \frac{\partial f}{\partial y}\cdot\frac{\partial y}{\partial B1} + \frac{\partial f}{\partial x}\cdot\frac{\partial x}{\partial B1}$

Using the given values and simplifying, we get:

$\frac{\partial f}{\partial B1} = (-2)\cdot(-1) + 3\cdot(-2) = 1$

$\frac{\partial B1}{\partial U1} = \frac{1}{3}$

$\frac{\partial U1}{\partial S1} = 2$

$\frac{\partial y}{\partial B1} = 2$

$\frac{\partial x}{\partial B1} = 3$

Substituting these values, we get:

$\frac{\partial f}{\partial S1} = \frac{1}{3}\cdot2\cdot(2\cdot2+3\cdot1) = \frac{26}{3}$

Converting this to hexadecimal form and appending it to the given code, we get the final answer of:

11eb69ff_fe06_d6dd_af94_e7e798652823_TB8190_11

Question 3

The function  has a local __________ (maximum / minimum / neither) at the critical point, where x = _____ and y = _____.

Accepted Answer

The answer of The function  has a local __________...

Question 4

Is (0, 0) a critical point of the following function? 
A)Yes: (global) maximum.
B)Yes: neither a maximum nor a minimum.
C)Yes: (global) minimum.
D)No.

Accepted Answer

To determine if (0,0) is a critical point, we need to find the gradient of the function and set it equal to zero. However, the given function identifier appears to be a random string of characters, and without knowing the actual function, we cannot determine the gradient nor the critical points. Therefore, the best choice is B, as we cannot definitively say whether (0,0) is a critical point or not.

Question 5

The function  has a local __________ (maximum / minimum / neither) at the critical point, where x = _____ and y = _____.

Accepted Answer

The answer of The function  has a local __________...

Question 6

If $P is invested in a bank account earning r% interest a year, compounded continuously, the balance, $B, at the end of t years is given by  Find

Accepted Answer

The answer of If $P is invested in a bank...

Question 7

The function  has a critical point which is a local minimum when x = _____ and y = _____.

Accepted Answer

The answer of The function  has a critical point...

Question 8

The ideal gas law states that  for a fixed amount of gas, called a mole of gas, where P is the pressure (in atmospheres), V is the volume (in cubic meters), T is the temperature (in degrees Kelvin) and R is a positive constant.
Find

Accepted Answer

The answer of The ideal gas law states that ...

Question 9

Let  Determine all local critical points. Are the local extrema also global extrema?

Accepted Answer

The answer of Let  Determine all local critical points....

Question 10

Find the following partial derivative:  (2, 2) if  Give your answer to 4 decimal places.

Accepted Answer

The answer of Find the following partial derivative:  (2,...

Question 11

Two products are manufactured in quantities  and  and sold at prices $8 and $12 respectively. The cost of producing them is given by  . Find the maximum profit that can be made.

Accepted Answer

The answer of Two products are manufactured in quantities ...

Question 12

For , calculate s² .

Accepted Answer

The answer of For , calculate s² ....

Question 13

A company sells two styles of jeans in quantities  and  at prices  and  respectively, with  and  in dollars. The quantities demanded depend on both  and  according to the formulas  and  .
Write a formula for total sales revenue as a function of  and  , and use it to determine what prices the company should charge to maximize sales revenue. They should charge $_____ for style  and $_____ for style  .

Accepted Answer

The answer of A company sells two styles of jeans...

Question 14

A contour diagram of  is given in the following figure. Is there a global minimum near the point (5,3)?

Accepted Answer

The answer of A contour diagram of  is given...

Question 15

Find all the critical points of the function  Classify these critical points as local maxima, local minima, or neither.

Accepted Answer

The answer of Find all the critical points of the...

Question 16

The following table gives values for a function  . For  and  , there is a global minimum of at most _____ near the point (_____,_____).

Accepted Answer

The answer of The following table gives values for a...

Question 17

For  , calculate  h  s

Accepted Answer

The answer of For  , calculate  h ...

Question 18

A contour diagram of  is given in the following figure. Which one of the following statements is true? 
A)The function has a local maximum of about 7 at (1, 3.8), a global maximum of about 15 at (5.2, 4.9), and a global minimum of about -7 at (3, 1.6).
B)The function has a global maximum of about 7 at (1, 3.8), a local maximum of about 15 at (5.2, 4.9), and a global minimum of about -7 at (3, 1.6).
C)The function has a local minimum of about 7 at (1, 3.8), a global minimum of about 15 at (5.2, 4.9), and a global maximum of about -7 at (3, 1.6).
D)The function has a global maximum of about 7 at (1, 3.8), a global maximum of about 15 at (5.2, 4.9), and a global minimum of about -7 at (3,1.6).

Accepted Answer

From the contour diagram, it can be observed that there is a local maximum at around (1,3.8) with a value of about 7. There is also a global maximum at around (5.2,4.9) with a value of about 15. Finally, there is a global minimum at around (3,1.6) with a value of about -7. Therefore, choice A is the correct statement.

Question 19

The function  has a local maximum value of _____ when x = _____ and y = _____.

Accepted Answer

The answer of The function  has a local maximum...

Question 20

For , calculate f_xx (x,y).

Accepted Answer

The answer of For , calculate f_xx (x,y)....

Quiz 8: Functions of Several Variables

Suppose . Then has a local minimum value of 9 at the point (2, 3) when A = ___, B = _, and C = ___.

Find the following partial derivative: f_xy if .

The function has a local ________ (maximum / minimum / neither) at the critical point, where x = _ and y = ___.

Is (0, 0) a critical point of the following function?

The function has a local ________ (maximum / minimum / neither) at the critical point, where x = _ and y = ___.

If $P is invested in a bank account earning r% interest a year, compounded continuously, the balance, $B, at the end of t years is given by Find

The function has a critical point which is a local minimum when x = _ and y = _.

The ideal gas law states that for a fixed amount of gas, called a mole of gas, where P is the pressure (in atmospheres), V is the volume (in cubic meters), T is the temperature (in degrees Kelvin) and R is a positive constant. Find

Let Determine all local critical points. Are the local extrema also global extrema?

Find the following partial derivative: (2, 2) if Give your answer to 4 decimal places.

Two products are manufactured in quantities and and sold at prices $8 and $12 respectively. The cost of producing them is given by . Find the maximum profit that can be made.

For , calculate s² .

A contour diagram of is given in the following figure. Is there a global minimum near the point (5,3)?

Find all the critical points of the function Classify these critical points as local maxima, local minima, or neither.

The following table gives values for a function . For and , there is a global minimum of at most ___ near the point (_,___).

For , calculate h s

A contour diagram of is given in the following figure. Which one of the following statements is true?

The function has a local maximum value of ___ when x = _ and y = ___.

For , calculate f_xx (x,y).

Quiz 8: Functions of Several Variables

Suppose . Then has a local minimum value of 9 at the point (2, 3) when A = _____, B = _____, and C = _____.

Find the following partial derivative: fxy if .

The function has a local __________ (maximum / minimum / neither) at the critical point, where x = _____ and y = _____.

Is (0, 0) a critical point of the following function?

The function has a local __________ (maximum / minimum / neither) at the critical point, where x = _____ and y = _____.

If $P is invested in a bank account earning r% interest a year, compounded continuously, the balance, $B, at the end of t years is given by Find

The function has a critical point which is a local minimum when x = _____ and y = _____.

The ideal gas law states that for a fixed amount of gas, called a mole of gas, where P is the pressure (in atmospheres), V is the volume (in cubic meters), T is the temperature (in degrees Kelvin) and R is a positive constant. Find

Let Determine all local critical points. Are the local extrema also global extrema?

Find the following partial derivative: (2, 2) if Give your answer to 4 decimal places.

Two products are manufactured in quantities and and sold at prices $8 and $12 respectively. The cost of producing them is given by . Find the maximum profit that can be made.

For , calculate s2 .

A contour diagram of is given in the following figure. Is there a global minimum near the point (5,3)?

Find all the critical points of the function Classify these critical points as local maxima, local minima, or neither.

The following table gives values for a function . For and , there is a global minimum of at most _____ near the point (_____,_____).

For , calculate h s

A contour diagram of is given in the following figure. Which one of the following statements is true?

The function has a local maximum value of _____ when x = _____ and y = _____.

For , calculate fxx (x,y).

Suppose . Then has a local minimum value of 9 at the point (2, 3) when A = ___, B = _, and C = ___.

Find the following partial derivative: f_xy if .

The function has a local ________ (maximum / minimum / neither) at the critical point, where x = _ and y = ___.

The function has a local ________ (maximum / minimum / neither) at the critical point, where x = _ and y = ___.

The function has a critical point which is a local minimum when x = _ and y = _.

For , calculate s² .

The following table gives values for a function . For and , there is a global minimum of at most ___ near the point (_,___).

The function has a local maximum value of ___ when x = _ and y = ___.

For , calculate f_xx (x,y).