Question

Suppose f '' is continuous on (−[infinity], [infinity])

Answer 1

Answer with Step-by-step explanation:

We are given that a function f(x) is continuous on ($-\infty,\infty$).

1.f'(-1)=0 and f''(-1)=-7

We have to find information about f.

When f'(-1)=0 and f''(-1)=-7 < 0

Then, 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  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.