confusing variables in a min/max

[Cuddles]

Suppose you know that f is a differentiable function on the interval (-h,h) when h>0 that f" exists on the interval (-h,h) and the f"<0 at x=0. Then you know that f has a ________ at x=0.
(the answer choices are local/absolute min/max or neither)

I just can't follow the variables. @_@

 

[Deleted member 4993]

Suppose you know that f is a differentiable function on the interval (-h,h) when h>0 that f" exists on the interval (-h,h) and the f"<0 at x=0. Then you know that f has a ________ at x=0.
(the answer choices are local/absolute min/max or neither)

I cannot understand your difficulty.

I just can't follow the variables. <--- what do you mean by that - "follow the variables"?

@_@

 

[Cuddles]

Um, I just don't know what to do or what's supposed to go where I guess.

 

[skeeter]

Suppose you know that f is a differentiable function on the interval (-h,h) when h>0 that f" exists on the interval (-h,h) and the f"<0 at x=0. Then you know that f has a ________ at x=0.
(the answer choices are local/absolute min/max or neither)

I just can't follow the variables. @_@

f''(0) < 0 tells you that f(x) is concave down at x = 0 ... that's all.

if the statement had said that f''(0) < 0 and f'(0) = 0, then there would be a max for f(x) at x = 0.

but, it didn't say that f'(0) = 0, unless you left that part out.

 

[Cuddles]

That's all the information, so I guess there just isn't enough info to know what it is. @_@