For what values of `x` the function `f(x)=x^(4)-4x^(3)+4x^(2)+40` is monotonic decreasing?

Options

A. `0lt x lt 1`
B. `1 lt xlt2`
C. `2 lt x lt3`
D. `4 lt x lt 5`

Answer

B

Explanation

Given `f(x)=x^(4)-4x^(3)+4x^(2)+40`
`impliesf'(x)=4x^(3)-12x^(2)+8x`
For monotonic decreasing `f'(x)lt0`
`impliesx(4x^(2)-12x+8)lt0`
`impliesx(x^(2)-3x+2)lt0`
`impliesx(x-1)(x-2)lt0`

`:.x epsilon(-oo,0)uu(1,2)`