Problem Statement

{2,4,6,8}
{1,3,5}
4 + 3
-1*4
-1*7
4 + 7
4*7
rand(2,9)
-7 - 1

Find the critical points and the intervals on which the function is increasing or decreasing. Use the First Derivative Test to determine whether the critical point is a local min or max (or neither).

 
Step 1

Question Sequence

Question 1

When f'(x) > 0 for all x on a defined open interval, then f is on that interval.

Correct.
Incorrect.

 
Step 2

Question Sequence

Question 4

Find f'(x).

where b = and c = .

Correct.
Incorrect.

 
Step 3

Use the two critical points to divide the real line into three intervals.

(-∞,-7),(-7,-4),(-4,∞)

To determine where f(x) is increasing or decreasing, pick an x-value in each interval, and identify the sign of f'(x).

Question Sequence

Question 6

Let's pick x1 = -8 in the first interval, x2 = -7 in the second interval, and x3 = 0 in the third interval. Fill in the table below with the appropriate sign.

Interval x-value Sign of f'(x)
(-∞,-4) -8
(-4,-7) -7
(-7,∞) 0
Correct.
Incorrect.

 
Step 4

The First Derivative Test for critical points states that for any critical point x = c:

Question Sequence

Question 8

If f'(x) changes sign from + to − at x = c, then f(c) is a local .

If f'(x) changes sign from − to + at x = c, then f(c) is a local .

Correct.
Incorrect.