Answer the following questions about the function whose derivative is given below. f′(x)=(x−5)^2(x+7)
a. what are the critical points of f?
b. On what intervals is f increasing or decreasing?
c. at what points, if any, does f assume local maximum and minimum values?

Question

Answer the following questions about the function whose derivative is given below. f′(x)=(x−5)^2(x+7)
a. what are the critical points of f?
b. On what intervals is f increasing or decreasing?
c. at what points, if any, does f assume local maximum and minimum values?

anonymous · Answer

please show all steps

primeralph · Answer

a. at f' = 0 or does not exist.
b. increasing while f' is positive and vise versa
c. f' = 0

anonymous · Answer

whats the difference between a and c?

terenzreignz · Answer

Well, a derivative which is equal to zero does not guarantee a local extremum...

anonymous · Answer

so how do you find a local extreme?

terenzreignz · Answer

First, tell me where the critical points are (the points where the derivative is zero or nonexistent)

anonymous · Answer

5 and -7

terenzreignz · Answer

Good :)
Now, the quickest way to find extrema... can you take the second derivative?
(This is already the first derivative, so just differentiate it once more)

anonymous · Answer

I don't know to for this one...

terenzreignz · Answer

Getting the derivative?

anonymous · Answer

yea

anonymous · Answer

is it 3(x^2-2x-15)?