Answer the following questions about the function whose derivative is f primef′(x)equals=x Superscript negative three fifths Baseline (x minus 3 )x− 3 5(x−3). a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? c. At what points, if any, does f assume local maximum and minimum values?

(a) The critical points of f are x=0 and x=3.

(b)f is decreasing on and f is decreasing on .

(c) Therefore the local minimum of f is at x=3

Step-by-step explanation:

Given function is

(a)

To find the critical point set f'(x)=0

The critical points of f are 0,3.

(b)

The interval are and .

To find the increasing or decreasing, taking two points one point from the interval (0,3) and another point .

Assume 1 and 4.

Now

and

Since 1∈ , f'(x)<0  and 4∈ , f'(x)>0

∴f is decreasing on and f is decreasing on .

(c)

Differentiating with respect to x

Now

and

Since f''(x)>0 at x=3

Therefore the local minimum of f is at x=3

a line is an defined derm because it

a)contains an infinite number of points b) can be used to create other geometric shapes c)describes something that does not have width or depth d) is a term that does not have a formal definition. a line is an undefined term because it: contains an infinite number of points.

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