(See Steps) (two points given for this one) "Graph" the function f(x)=2x^5/3-5x^4/3. Use the fact that f'(x)=(10)/(3)x^1/3(x^1/3-2) , f''(x)=(20(x^1/3-1))/(9x)^2/3
Question: (two points given for this one)
"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:
- Domain.
- x- and y-intercepts.
- Horizontal asymptotes, if any.
- Vertical asymptotes, if any.
- Critical numbers, intervals when the function is increasing and decreasing.
- Inflection points, concavity.
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