You are given a function F is defined and continuous at every real number. You a

Question

You are given a function F is defined and continuous at every real number. You are also given that f' (-2) =0, f'(3.5)=0, f'(5.5)=0 and that f'(2) doesn't exist. As well you know that f'(x) exists and is non zero at all other values of x. Use this info to explain precisely how to locate abs. max and abs. min values of f(x) over interval [0,4]. Use the specific information given in your answer.

Explanation / Answer

This is relatively a bit easy one. Critical points are -2,3.5,5.5 there is an asymptode at x=2. (f'(2) doesn't exist) So the critical points before and after x=3 are of the opposite nature, ie if one is maximum the other is minimum and vice versa there are two cases: 1) if f(2)->+inf x=-2 is local max x=-2 is local min x= 2.5 is local max 2) 1) if f(2)->-inf x=-2 is local min x=-2 is local max x= 2.5 is local min Hope my detailed explanation helps :)

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