Question

The maximum value of the function $f(x)=2x^3-15x^2+36x-48$ on the set $A=\left\{x\left|x^2+20\le 9x\right|\right\}$ is

Answer 1

Answer: 7

$f^{\prime }(x)=6(x-2)(x-3)$
so $f(x)$ is increasing $in(3,\infty )$
Also, $A=\{4\le x\le 5\}$
$\therefore f_{\max }=f(5)=7$