Mathematics - Application of Derivative Question with Solution | TestHub

The given function is $f(x)=2x^3-15x^2+36x-48$ and $A=\{x\mid x^2+20\le 9x\}$.

$A=\{x\mid x^2-9x+20\le 0\}$

$A=\{x\mid (x-4)(x-5)\le 0\}$.

$A=[4,5]$.

Also, $f^{\prime }(x)=6x^2-30x+36=6(x^2-5x+6)=6(x-2)(x-3)$.

Clearly," $x\in A$, $f^{\prime }(x)>0$.

$f$ is a strictly increasing function on

The maximum value of $f$ on $A$

$$f(5)=2(5{)}^3-15(5{)}^2+36(5)-48=250-375+180-48=7$$