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help? derivatives?

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asked May 6, 2015 in CALCULUS by anonymous

1 Answer

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6)

Step 1:

The function is .

Differentiate on each side with respect to .

Find the critical points.

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

Thus, the critical points exist when .

Equate  to zero.

, and .

The critical points are , and .

The test intervals are , , and .

The function is increasing on the intervals and image.

The function is decreasing on the intervals and .

answered May 6, 2015 by david Expert

Contd..

Step 2:

.

Differentiate on each side with respect to .

image

Find the inflection points.

Equate to zero.

image

The inflection points are at image.

The test intervals are image, image and image.

The graph is concave up on the interval image and image.

The graph is concave down on the interval image.

Step 3:

Graph the function :

Solution:

The function is increasing on the intervals  and image.

The function is decreasing on the intervals and .
 

The graph is concave up on the interval image and image.

The graph is concave down on the interval image.

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