help-derivative-ex

Question

Answer 1

(8)

Step 1:

The function is .

Increasing-Decreasing Test:

1) If is increasing at .

2) If is decreasing at .

2) If is inconclusive at .

Apply derivative on each side with respect to .

.

Step 2:

Determine whether the function is increasing, decreasing or not changing at .

Substitute in .

.

The function is increasing at .

Solution:

is increasing at .

Answer 2

(9)

Step 1:

The function is .

Increasing-Decreasing Test:

1) If is increasing at .

2) If is decreasing at .

2) If is inconclusive at .

Apply derivative on each side with respect to .

Apply product rule in derivatives: .

.

Step 2:

Determine whether the function is increasing, decreasing or not changing at .

Substitute in .

.

.

The function is not changing at .

Solution:

The function is not changing at .