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For what values of x the function f(x)=x...

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

A

`0ltxlt1`

B

`1ltxlt2`

C

`2ltxlt3`

D

`4ltxlt5`

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)=x^(4)-4x^(3)+4x^(2)+40`
`f'(x)=4x^(3)-12x^(2)+8x`
`f'(x)=4x(x^(2)-3x+2)`
`=4x(x-1)(x-2)`
for `f(x)` is monotonic decreasing `f'(x)lt0`
`:.x(x-1)(x-2)lt0`
which is possible when `xlt0` of `1ltxlt2`.
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