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

Options

A. `-(3)/(2)log_(10)^(3)`
B. `1+log10^(3)`
C. `log10^(3)`
D. `(3)/(2)log10^(3)`

Answer

2

Explanation

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`