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The global maximum value of f(x0=(log)(1...

The global maximum value of `f(x0=(log)_(10)(4x^3-12 x^2+11 x-3),x in [2,3],` is `-3/2(log)_(10)3` (b) `1+(log)_(10)3` `(log)_(10)3` (d) `3/2(log)_(10)3`

A

`(-3)/2log_(10)3`

B

`1+log_(10)3`

C

`log_(10)3`

D

`3/2log_(10)3`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `g(x)=4x^(3)-12x^(2)+11x-3`
`:.g^(')(x)=10x^(2)-24x+11`
`=12(x-1)^(2)-1gt0` for `0epsilon [2,3]`
`f(x)_(max)=f(3)=log_(1)(4xx27-12xx9-11xx3-3)`
`=log_(10)30=1+log_(10)3`
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