Find the absolute maximum and minimum values of f(x) = x2/3 on the int | Basic Mathematics 0

Basic Mathematics05 marksNumerical: absolute max minAbsolute maximum and minimum values

Find the absolute maximum and minimum values of $f(x) = x^{2/3}$ on the interval $[-2, 3]$ . [5]

Find the absolute maximum and minimum values of $f(x) = x^{2/3}$ on the interval $[-2, 3]$. [5]

Function: $f(x) = x^{2/3}$ - Interval: $[-2, 3]$ (closed) $f'(x) = \frac{2}{3}x^{-1/3} = \frac{2}{3\sqrt[3]{x}}$ Set $f'(x) = 0$ : The numerator is $2 \neq 0$ , so $f'(x)$ is never zero. Where $f'(x)$ is undefined: $\sqrt[3]{x} = 0 \Rightarrow x = 0$ . Since $x = 0$ lies in $[-2, 3]$ , it is a cr...

Function: $f(x) = x^{2/3}$ - Interval: $[-2, 3]$ (closed) $$f'(x) = \frac{2}{3}x^{-1/3} = \frac{2}{3\sqrt[3]{x}}$$ Set $f'(x) = 0$: The numerator is $2 \neq 0$, so $f'(x)$ is never zero. Where $f'(x)$ is undefined: $\sqrt[3]{x} = 0 \Rightarrow x = 0$. Since $x = 0$ lies in $[-2, 3]$, it is a cr...

Find the absolute maximum and minimum values of f(x) = x2/3 on the interval [-2, 3].