# The function F(x)= x^( 2/3) is continuous everywhere. How do you find the maximum and minimum values on [-1,2]?

Jan 25, 2017

${\min}_{x \in \left[- 1 , 2\right]} F \left(x\right) = F \left(0\right) = 0$

${\min}_{x \in \left[- 1 , 2\right]} F \left(x\right) = F \left(2\right) = \sqrt[3]{4}$

#### Explanation:

If we calculate the derivative:

$F ' \left(x\right) = \frac{2}{3} {x}^{- \frac{1}{3}}$

we can see that $F \left(x\right)$ is decreasing for $x < 0$ and increasing for $x > 0$. So, in the interval [-1,2] the minimum will be reached for $x = 0$ and the maximum in $x = 2$.