Answer
a. See graph.
b. No vertical tangent.
Work Step by Step
a. See graph; it appears to have a vertical tangent at $x=0$
b. Evaluate the limit: $\lim_{h\to0}\frac{f(0+h)-f(0)}{h}=\lim_{h\to0}\frac{h^{5/3}-5h^{2/3}}{h}=\lim_{h\to0}(h^{2/3}-5h^{-1/3})$.
As $\lim_{h\to0^+}(h^{2/3}-5h^{-1/3})=-\infty$ and $\lim_{h\to0^-}(h^{2/3}-5h^{-1/3})=\infty\ne \lim_{h\to0^+}(h^{2/3}-5h^{-1/3})$
the function does not have a vertical tangent at $x=0$
