help? (Derivatives and Funcrions)

Question

Answer 1

(10)

Step 1:

The function is .

Differentiate on each side with respect to .

Find the critical points.

Since it is a polynomial it is continuous at all the point.

Thus, the critical points exist when .

Equate to zero.

and .

The critical points are and .

Comments

Step 2:

The test intervals are .

Therefore the function is increasing on the intervals and .

The function is decreasing on the interval .

in the interval of .

So the function is increasing at .

Solution :

The function is increasing at .

Answer 2

(11)

Step 1:

The function is .

From the results of (10) :

The function is increasing on the intervals and .

The function is decreasing on the interval .

x = 2 in the interval of .

So the function is increasing at x = 2.

Solution :

The function is increasing at x = 2.

Answer 3

(12)

Step 1:

The function is .

From the results of (10) :

The function is increasing on the intervals and .

The function is decreasing on the interval .

So the graph is continuously changing.

Solution :

The graph is continuously changing.