Question:

“Graph” the function \[f(x)=2{{x}^{5/3}}-5{{x}^{4/3}}\]. Use the fact that

\[\begin{aligned} & {f}'(x)=\frac{10}{3}{{x}^{1/3}}({{x}^{1/3}}-2) \\ & {f}''(x)=\frac{20({{x}^{1/3}}-1)}{9{{x}^{2/3}}} \\ \end{aligned}\]

Find:

a) Domain.

b) x- and y-intercepts.

c) Horizontal asymptotes, if any.

d) Vertical asymptotes, if any.

e) Critical numbers, intervals when the function is increasing and decreasing.

f) Inflection points, concavity.