Question

The function $f\left(x\right)=2\log (x-2)-x^2+4x+1$ increase in the interval .

• A. $(1,2)$
• B. $(2,3)$
• C. $\left(\frac{5}{2},3\right)$
• D. $(2,4)$

Answer 1

Answer: (B)

$(2,3)$

$f\left(x\right)=2\log (x-2)-x^2+4x+1$
$f\left(x\right)$ is defined for $x>2$
$f^{{}^{\prime }\left(x\right)}=\frac{2}{(x-2)}-2x+4$
$f\left(x\right)=-2x^2+8x-6$
$f\left(x\right)=-(2x^2-8x+6)$
$f\left(x\right)$ is increasing in $(1,3)$
But because of domain restriction function is increasing in the interval $(2,3)$