Question

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

Answer 1

`min_(x in [-1,2] ) F(x) = F(0) = 0`

`min_(x in [-1,2] ) F(x) = F(2) = root(3)(4)`

Explanation:

If we calculate the derivative:

`F'(x) =2/3x^(-1/3)`

we can see that `F(x)` 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`.