Information:

Given $\displaystyle f: [-\sqrt\pi, \sqrt\pi] \rightarrow [-1,1]$ defined by $\displaystyle f(x)= sin(x^2)$

The problem:

Find a $\displaystyle \delta$ so that $\displaystyle |x - y| \leq \delta$ implicates that $\displaystyle |f(x) - f(y)| \leq 0.1$ for all $\displaystyle x$ and $\displaystyle y$ in $\displaystyle [-\sqrt\pi, \sqrt\pi]$

I was told that the mean value theorem can be used to find our $\displaystyle \delta$. Don't know how though. Any ideas on how to proceed?