My task is as follows:

Let $\displaystyle f(x) = x^2 \text{for } x \geq 0 \wedge f(x) = 0 \text{for } x < 0. $

B. Show that f is differentiable at $\displaystyle x = 0. $

C. Calculate $\displaystyle f' \text{on } \mathbb{R}. $

Any help will be greatly appreciated.

-the Doctor