Function differentiable at least once properties

[Mattiatore]

Given a function f: R to R and differentiable at least once, if f(x) is even then is f'(0)=0? If f'(x)>0 for each x different from 0 and f'(0)=0 then can f(x) not be strictly monotonically increasing? Only one of those is true and i think the first one but i am not sure...

 

[Deleted member 4993]

Given a function f: R to R and differentiable at least once, if f(x) is even then is f'(0)=0? If f'(x)>0 for each x different from 0 and f'(0)=0 then can f(x) not be strictly monotonically increasing?

Only one of those is true and i think the first one but i am not sure...

I am not understanding - what do you mean by that.

Please respond with a bit more detail.

 

[Mattiatore]

Sorry. I found it and a multiple choice quiz therefore, unless is wrong, only one of those two statements is true. I think it's true because it works for cos(x) and x^2 but i cannot really prove it or contradict the other one...

 

[stapel]

Sorry. I found it and a multiple choice quiz therefore, unless is wrong, only one of those two statements is true. I think it's true because it works for cos(x) and x^2 but i cannot really prove it or contradict the other one...

Um...

Please provide the full and exact text of the exercise, clearly stating which parts are "question" and which parts are "answer options". Then separately please provide your reasoning. Thank you!