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

The global maximum value of `f(x)=(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)/(2)log_(10)^(3)`

B

`1+log10^(3)`

C

`log10^(3)`

D

`(3)/(2)log10^(3)`

Text Solution

Verified by Experts

The correct Answer is:
2
Let `g(x) =4x^(3)-12x^(2)+11-3`
`therefore g(x) =12x^(2)-24x+11`
`=12(x-1)^(2)-1`
`gt0 for x in [2,3]`
Thus g(x) is increasing in [2,3]
Thus g(X) is increasing in [2,3]
`f(x)_(max)=f(x)3=log_(10)4(27)-12(9)+11(3)-3)`
`=log_(10)(30)`
`=1+log_(10)3`
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