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The function f defined by f(x) = x^(...

The function f defined by
`f(x) = x^(3) - 6x^(2) - 36 x + 7` is increasing , if

A

xgt2 and also xgt6

B

xgt2 annd also x`lt`6

C

`xlt-2` and also `xlt6`

D

`xlt-2` and also `xgt6`

Text Solution

Verified by Experts

The correct Answer is:
D
Given `f(x)=x^(3)-6x^(2)-36x+7`
`impliesf'(x)=3x^(2)-12x-36`
For f(x) to be increasing f'(x)gt0
`implies3x^(2)-12x-36gt0`
`implies(x-6)(x+2)gt0`
`impliesxgt6 and xlt-2`
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