The function `f(x)=2log(x-2)-x^2+4x+1` increases on the interval (a) `(1,\ 2)` (b) `(2,\ 3)` (c) `(1,\ 3)` (d) `(2,\ 4)`

Explanation

Answer is (2,3)

We have:
`
f(x)=2 log (x-2)-x^{2}+4 x+1`
`
Domain of {f}(x) is (2, infty).`
`

f^{prime}(x)=frac{2}{x-2}-2 x+4 `
`
=frac{2-2 x^{2}+4 x+4 x-8}{x-2} `
`
=frac{-2 x^{2}+8 x-6}{x-2} `
`
...