Problem Statement

rand(2,9)
round(7*sqrt(2),2)

Find the critical points of f(x) = 7·sin(x) +7·cos(x) and determine the extreme values on .

 
Step 1

Question Sequence

Question 1

A number c in the domain of f is called a critical point if f'(c) = or where f'(c).

Correct.
Incorrect.

Question 2

The extreme values (absolute maximum and absolute minimum) of a continuous function on a closed interval occur either at a of the function or at the of the closed interval.

Correct.
Incorrect.

 
Step 2

Thus, we need to find the critical points of f(x) = 7·sin(x) +7·cos(x) in and then compare the function values at these critical points with the function values at the endpoints of to find the extreme values.

Question Sequence

Question 3

Find f'(x).

f(x) = 7·sin(x) +7·cos(x)

f'(x) =

Correct.
Incorrect.

Question 4

f'(x) is .

Correct.
Incorrect.

 
Step 3

Solve f'(x) = 0 for to find any critical points, c.

Question Sequence

Question 5

f'(x) = 0

7·sin(x) + 7·cos(x) = 0

sin(x) = cos(x)

tan(x) =

Correct.
Incorrect.

Question 6

Thus, the critical point on that satisifes this equation is

c = .

Correct.
Incorrect.

 
Step 4

Compare the values of f(x) = 7·sin(x) + 7·cos(x) at the critical point x = and the endpoints of . The greatest value is the absolute maximum and the smallest value is the absolute minimum of f(x) on .

Question Sequence

Question 7

.

.

.

(Round your answers to two decimal places.)

Correct.
Incorrect.

 
Step 5

Question Sequence

Question 8

The minimum value of f is .

The maximum value of f is .

(Round your answers to two decimal places.)

Correct.
Incorrect.