What is / are the critical points (s) of the function `f(x) = x^(2//3) (5-2x)` on the interval [-1,2]?

Options

A. 1 only
B. 0,1
C. `3/2` only
D. `0,3/2`

Answer

A

Explanation

`f(x) =x^(2//3)(5-2x)`
or f(x)`=5x^(2//3)-2x^(5//3)`
`or f(x) =(10)/(3)(x^(-1//3)-x^(2//3))`
To get the critical value
f(x)=0
so `x^(-1//3) - x^(2//3) =0 rarr x^(-1//3)(1-x)=0`
`rarr 1-x=0 as x^(1//3) ne 0`
or x =1 is the only value in the interval [-1,2]