Given:

$\displaystyle f(0)=f(2)=0$

$\displaystyle f'(x) < 0$ if $\displaystyle x < 1$

$\displaystyle f'(1)=0$

$\displaystyle f'(x) > 0$ if $\displaystyle x > 1$

$\displaystyle f''(x) > 0$

How can I sketch a graph of the function $\displaystyle f$ given these characteristics? How would it look and how can I prove this?