All possible value of `f(x)=(x+1)^(1/3)-(x-1)^(1/3)` on [0,1] is 1 (b) 2 (c) 3 (d) `1/3`

Options

A. 0
B. 1
C. 2
D. -1

Answer

C

Explanation

Given `f(x)=(x+1)^(1//3)-(x-1)^(1//3)`
`impliesf'(x)=1/3(x+1)^(-2//3)-1/3(x-1)^(-2//3)`
Now put `f'(x)=0`
`implies 1/3(x+1)^(-2//3)=1/3(x=1)^(-2//3`
`implies (x-1)^(2)=(x+1)^(2)impliesx=0`
At `x=0,f''` is negative, so it maximum
Now `f(0)=(0+1)^(1//3) -(0-1)^(1//3)=2`
and `f(1)=(2)^(1//3)-(a)^(1//3)=2^(1//3)`
Hence, greatest value is 2.