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help? (Derivatives and Funcrions)

0 votes

asked Apr 28, 2015 in CALCULUS by anonymous

3 Answers

0 votes

(10)

Step 1:

The function is .

Differentiate on each side with respect to .

image

Find the critical points.

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

Thus, the critical points exist when image.

Equate image to zero.

image

and .

The critical points are and .

answered Apr 28, 2015 by yamin_math Mentor

Step 2:

The test intervals are .

Therefore the function is increasing on the intervals and .

The function is decreasing on the interval .

image in the interval of .

So the function is increasing at image.

Solution :

The function is increasing at image.

0 votes

(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.

answered Apr 29, 2015 by yamin_math Mentor
0 votes

(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.

answered Apr 29, 2015 by yamin_math Mentor

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