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!!

Re: Help with Calculus (undergraduate mathematics)

Quote:

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.

Think about $\displaystyle f(x)=x^3$ on $\displaystyle [0,1]$.

Re: Help with Calculus (undergraduate mathematics)

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]

Re: Help with Calculus (undergraduate mathematics)

Quote:

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]

The function $\displaystyle f(x) = \left\{ {\begin{array}{rl} {{x^2}\sin \left( {{x^{ - 2}}} \right),}&{0 < x \leqslant b} \\ {0,}&{x = 0}\end{array}} \right.$ has that property.

$\displaystyle f(0)=0~\&~f'(0)=0$ but $\displaystyle f(0)$ is neither a min nor a max in any neighborhood of $\displaystyle 0$.

Re: Help with Calculus (undergraduate mathematics)

Ok, I can see it now. Thanks!!

Re: Help with Calculus (undergraduate mathematics)

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