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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

`x gt 2` and also `x gt 6`

B

`x gt 2` and also `x lt 6`

C

`x gt -2` and also `x lt 6`

D

`x lt -2` and also `x gt 6`

Text Solution

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The correct Answer is:
D
Given, `f(x) = x^(3) - 6x^(2) - 36x + 7`
` rArr f'(x) = 3x^(2) - 12 x -36`
For f(x) to be increasing `f'(x) gt 0`
`rArr 3(x^(2) -4x -12) gt 0`
`rArr (x-6) (x+2) gt0`
`rArr x gt 6`
and `x lt -2`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 17-MATHEMATICS
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