The critical points of the function `f(x)=(x-2)^(2//3)(2x+1)` are

Options

A. 1 and 2
B. 1 and `-1/2`
C. `-1 and 2`
D. 1

Answer

A

Explanation

We have
`f(x)=(x-2)^(2//3)(2x-1)`
`rArr f'(x)=2/3(x-2)^(1//3)(2x+1)+2(x-2)^(2//3)`
Clearly , f(x) is not defined at x=2
So, x=2 is a critical point , Another critical point is given by
f'(x)=0
`rArr (2//3)(x-2)^(-1//3)(2x+1)+2(x-2)^(2//3)=0`
`rArr 2x-1=-3(x-2)rArrx=1`
Hence 1 and 2 are two critical points of f(x)