Answer
a. See graph,
b. vertical tangent at $x=0$
Work Step by Step
a. See graph; it appears to have a vertical tangent at $x=0$
b. Evaluate the limit at $x=0$: $\lim_{h\to0^-}\frac{f(0+h)-f(0)}{h}=\lim_{h\to0^-}\frac{-\sqrt {|h|}-0}{-|h|}=\lim_{h\to0^-}\frac{-1}{-\sqrt {|h|}}=\infty$ and $\lim_{h\to0^+}\frac{f(0+h)-f(0)}{h}=\lim_{h\to0^-}\frac{\sqrt {h}-0}{h}=\lim_{h\to0^-}\frac{1}{\sqrt {h}}=\infty$, thus the function has a vertical tangent at $x=0$
