Help with Calculus (undergraduate mathematics)

Hi, I'm a mathematics student and I need help with a simple problem:

Given a C1 function f:[a,b]-->R, with a right-hand derivative f'(a) on a. Proof if the following statement is true or false.
If f'(a)=0, then f has a local maximum or a local minimum on a.

Thanks very much!!

Quote:

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Originally Posted by yannt

Hi, I'm a mathematics student and I need help with a simple problem:

Given a C1 function f:[a,b]-->R, with a right-hand derivative f'(a) on a. Proof if the following statement is true or false.
If f'(a)=0, then f has a local maximum or a local minimum on a.

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Think about on .

That is exactly what I did in the first place, but the teacher wrote the following:

You have to place the function on an interval of the type [0,b], in your example, there is a local minimum on 0 in the interval [0,b]

Quote:

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Originally Posted by yannt

That is exactly what I did in the first place, but the teacher wrote the following: You have to place the function on an interval of the type [0,b], in your example, there is a local minimum on 0 in the interval [0,b]

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The function has that property.
but is neither a min nor a max in any neighborhood of .

Ok, I can see it now. Thanks!!

need some help in this please!!
is given the function {y=sin2x/x for x different from 0} or {y=2a for x=o}. find "a" if this function is continuous everywhere.
please help