Question 1

Find the linearization of the given function centered at  , and use it to estimate  . 
A)  
B)

Accepted Answer

A)  B)

Question 2

A ball produced on an assembly line is supposed to have a volume of   . Use linearization to estimate the maximum allowable error in the radius  if the volume of the sphere must have an error of less than   .

Accepted Answer

Radius error must be less than  inch.

Question 3

By Rolle's Theorem the equation  has at most two roots.

Accepted Answer

True

Question 4

The radius  of a sphere is measured at 4 m. Use linear approximation to estimate the maximum error in the surface area of the sphere if  is accurate to within  m.

Accepted Answer

The answer of The radius  of a sphere is...

Question 5

Find the maximum value  and the minimum value  of the function in the given interval 
A)  
B)

Accepted Answer

The answer of Find the maximum value  and the...

Question 6

Find the maximum value  and the minimum value  of the function in the given interval 
A)  
B)

Accepted Answer

The answer of Find the maximum value  and the...

Question 7

Find the maximum value  and the minimum value  of the function in the given interval or in its natural domain 
A)  
B)  
C)

Accepted Answer

The answer of Find the maximum value  and the...

Question 8

Estimate  using linear approximation.

Accepted Answer

The answer of Estimate  using linear approximation....

Question 9

The minimum and maximum of which of the following functions does not occur at a critical point in the open interval:
A) 
B) 
C) 
D) 
E)

Accepted Answer

The minimum and maximum of a continuous function on a closed interval will always occur at either a critical point or an endpoint. Therefore, the fact that the minimum and maximum of function C do not occur at a critical point in the open interval suggests they occur at the endpoints. In contrast, for the other options it is possible that the minimum or maximum occurs at a critical point within the open interval.

Question 10

Let  . By Rolle's Theorem we can prove that
A)  has 11 real roots.
B)  has at most 3 real roots.
C)  has no real roots.
D)  has at most 2 real roots.
E)  has 10 real roots.

Accepted Answer

The answer of Let  . By Rolle's Theorem we...

Question 11

Find the maximum value  and the minimum value  of the function in the given interval. 
A)  
B)

Accepted Answer

The answer of Find the maximum value  and the...

Question 12

Each of the following functions restricted to the given interval attains a minimum and maximum value. Which attain their maximum or minimum value at a point in the interior of the interval?
A)  on  
B)  on  
C)  on  
D)  on

Accepted Answer

The answer of Each of the following functions restricted to...

Question 13

Estimate the length of the hypotenuse in a right triangle with sides 3 and 4.01, using the linear approximation for  .

Accepted Answer

The answer of Estimate the length of the hypotenuse in...

Question 14

Find the linearization of the given function centered at  and use it to estimate  . 
A)  
B)

Accepted Answer

The answer of Find the linearization of the given function...

Question 15

Estimate the roots of the equation  to three decimal places using the linear approximation for  .

Accepted Answer

The answer of Estimate the roots of the equation ...

Question 16

Estimate the roots of the equation  using the linear approximation for  at  .

Accepted Answer

The answer of Estimate the roots of the equation ...

Question 17

Estimate the roots of the equation  using the linear approximation for  .

Accepted Answer

The answer of Estimate the roots of the equation ...

Question 18

Estimate the value of  using the linear approximation and find the error using a calculator.

Accepted Answer

The answer of Estimate the value of  using the...

Question 19

Suppose that a function  satisfies the following equation for small values of  :  .
Also,  and  . 
A) Find the linearization of  at  . 
B) Replace  by its linearization and find a quadratic equation for  . 
C) Estimate the roots of the quadratic equation in  to 4 decimal digits using linearization for  .

Accepted Answer

The answer of Suppose that a function  satisfies the...

Question 20

Find all the critical points of the function
A)  
B)

Accepted Answer

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

Quiz 4: Applications of the Derivative

Find the linearization of the given function centered at , and use it to estimate . A) B)

A ball produced on an assembly line is supposed to have a volume of . Use linearization to estimate the maximum allowable error in the radius if the volume of the sphere must have an error of less than .

By Rolle's Theorem the equation has at most two roots.

The radius of a sphere is measured at 4 m. Use linear approximation to estimate the maximum error in the surface area of the sphere if is accurate to within m.

Find the maximum value and the minimum value of the function in the given interval A) B)

Find the maximum value and the minimum value of the function in the given interval A) B)

Find the maximum value and the minimum value of the function in the given interval or in its natural domain A) B) C)

Estimate using linear approximation.

The minimum and maximum of which of the following functions does not occur at a critical point in the open interval:

Let . By Rolle's Theorem we can prove that

Find the maximum value and the minimum value of the function in the given interval. A) B)

Each of the following functions restricted to the given interval attains a minimum and maximum value. Which attain their maximum or minimum value at a point in the interior of the interval? A) on B) on C) on D) on

Estimate the length of the hypotenuse in a right triangle with sides 3 and 4.01, using the linear approximation for .

Find the linearization of the given function centered at and use it to estimate . A) B)

Estimate the roots of the equation to three decimal places using the linear approximation for .

Estimate the roots of the equation using the linear approximation for at .

Estimate the roots of the equation using the linear approximation for .

Estimate the value of using the linear approximation and find the error using a calculator.

Suppose that a function satisfies the following equation for small values of : . Also, and . A) Find the linearization of at . B) Replace by its linearization and find a quadratic equation for . C) Estimate the roots of the quadratic equation in to 4 decimal digits using linearization for .

Find all the critical points of the function A) B)