Question

The maximum value of $f\left(x\right)=\frac{8}{9x^2-6x+5}$ in its domain is

Answer 1

$f\left(x\right)$ will be maximum when $9x^2-6x+5$ is minimum.
Let $g\left(x\right)=9x^2-6x+5,a=9(>0)$
$\therefore$ Minimum value of $g\left(x\right)$
$\frac{4ac-b^2}{4a}=\frac{180-36}{36}=4$

$\therefore$ Maximum value of $f\left(x\right)=\frac{8}{4}=2$