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The maximum value of function f(x)=x^3-1...

The maximum value of function `f(x)=x^3-12 x^2+36 x+17` in the interval `[1,10]` is `17` b. `177` c. `77` d. none of these

A

17

B

177

C

77

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `f(x)=x^(3)-12x^(2)+36x+17`
`:. f'(x)=3x^(2)-24x+36=0`
For maximum, put `f'(x)=0`
`rArr 3x^(2)-24x+36=0`
`rArr (x-2)(x-6)=0`
`rArr x=2,6`
Again `f''(x)=7x-24` is negative at x=2
So, that `f(6)=17,f(2)=49`
At the end point. `f(1)=42`, f(10)=177`
So that, f(x) has it maximum value 177.
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