If `x` satisfies the condition `f(x)={x:x^2+3 0le11x}` then maximum value of function `f(x)=3x^3-18x^2-27x-40` is equal to (A) `-122` (B) `122` (C) `222` (D) `-222`

Options

A. 222
B. `-222`
C. 122
D. `-122`

Answer

C

Explanation

For given region : `x^2-11x+30 le 0 rArr (x-5)(x-6) le 0 rArr x in [5,6]`
Also , `f'(x)=9x^2-36x+27=9(x^2-4x+3)=9(x-1)(x-3) > 0` for [5.6]
`rArr` f(x) is monotonically increasing in [5,6]
So maximum value of `f(x)=f(6)=(3(6^3)-18(6^2) + 27xx6-40)` = 122