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help-derivatives? shape of?

0 votes

asked May 6, 2015 in CALCULUS by anonymous

3 Answers

0 votes

(5)

Step 1:

The function is .

Differentiate on each side with respect to .

.

Step 2:

Find the critical points.

Since 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 .

Solution :

The critical points are and .

answered May 6, 2015 by Anney Mentor
0 votes

(6)

Step 1:

The function is .

.

The critical points are and .

The test intervals are , and .

The function is increasing on the intervals and .

The function is decreasing on the interval .

Solution :

The function is increasing on the intervals and .

The function is decreasing on the interval .

answered May 6, 2015 by Anney Mentor
edited May 6, 2015 by Anney
0 votes

(7)

Step 1:

The function is .

The critical points are and .

The function is increasing on the intervals and .

The function is decreasing on the interval .

Find the local maximum and local minimum.

The function has a local maximum at , because changes its sign from positive to negative.

Substitute in .

Local maximum is .

The function has a local minimum at , because changes its sign from negative to positive.

Local minimum is .

Solution :

Local maximum is .

Local minimum is .

answered May 6, 2015 by Anney Mentor
reshown May 6, 2015 by casacop

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