Answer
a. See graph, vertical tangent at $x=0$
b. Yes.
Work Step by Step
a. See graph; it appears to have a vertical tangent at $x=0$
b. Evaluate the limit: $\lim_{h\to0}\frac{f(0+h)-f(0)}{h}=\lim_{h\to0}\frac{h^{3/5}-0}{h}=\lim_{h\to0}\frac{1}{h^{2/5}}$
As $\lim_{h\to0^+}\frac{1}{h^{2/5}}=\infty$ and $\lim_{h\to0^-}\frac{1}{h^{2/5}}=\infty= \lim_{h\to0^+}\frac{1}{h^{2/5}}$, thus the function has a vertical tangent at $x=0$.
