Q:

Suppose f '' is continuous on (βˆ’[infinity], [infinity])(1) If f '(-1) = 0 and f ''(-1) = -7, what can you say about f?a)At x = -1, f has local maximum.b)At x = -1, f has a local minimum. c) At x = -1, f has not a maximum or minimum.d) There is not enough information.(2) If f '(4) = 0 and f ''(4) = 0, what can you say about f?a) At x = 4, f has local maximum.b) At x = 4, f has a local minimum. c) At x = 4, f has not a maximum or minimum.d) There is not enough information.

Accepted Solution

A:
Answer with Step-by-step explanation:We are given that a function f(x) is continuous on ([tex]-\infty,\infty[/tex]).1.f'(-1)=0 and f''(-1)=-7We have to find information about f.When f'(-1)=0 and f''(-1)=-7 < 0Then, function is maximum at x=-1.Therefore, at x=-1, f has local maximum.Answer:a)at x=-1 ,f has local maximum.2.) if f'(4)=0 and f''(4)=0 We know that when f''(x)=0 then test fails Β then the function has not maximum or minimum.Therefore, at x=4 , f has not a maximum or minimum.Answer:c) at x=4, f has not a maximum or minimum.