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

sorry bro , takes time to explain

anonymous · Answer

It's okay, I want to understand it so take your time

rajee_sam · Answer

Critical points are those where the slope = 0 ( aka The derivative does not exist). So to find the critical point put derivative = 0 and find values of x. 

$$(x-5)^{2}(x+7) = 0 $$ 

x = 5, 5 , -7

anonymous · Answer

Okay, but how do you tell where they're increasing or decreasing?

rajee_sam · Answer

I am having server problem , my connection is very slow, stay in touch I will explain everything shortly

anonymous · Answer

okay

anonymous · Answer

3(x^2-2x-15)

rajee_sam · Answer

A function is increasing in an interval if its first derivative is poitive in that interval.
i.e (f'(x) > 0) .

A function is decreasing in an interval if its first derivative is negative in that interavl. 
i.e. (f'(x) < 0 )

Since we know our critical values where our derivative is zero we set up the intervals and give test values in each interval to determine the sign of the derivative.

rajee_sam · Answer

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