# Derivatives?

#### cuenc

Hello everyone, i tried to solve this :

Theorem 4.10 goes like this . Let f :[a, b]→R be continuous and differentiable on (a, b). If f '(x)≥0 for all x∈(a, b), then f is monotonically increasing. Likewise, f is strictly increasing, monotonically decreasing, and strictly decreasing if ‘≥’ is replaced by ‘>’, ‘≤’, and ‘<’, resp.
i tried fucntions like x^2 , x^3, sin(x), cos(x), but none seemed to work ( FAILED TO PROVE THAT F'(X)>0)
Any help would be greatly appreciated

#### skeeter

Math Team
Consider the function $f(x)=x^3$ over the interval $[-1,1]$. For all $x_1 < x_2 \in (-1,1)$, $f(x_1) < f(x_2)$ which satisfies the definition of a strictly increasing function (see link) ... and $f’(0) = 0$