The maximum value of the function $f(x)=2 x^3-15 x^2+36 x-48$ on the set $A=\left\{x \mid x^2+20 \leq 9 x\right\}$ is P-2, $(4,-1)$, 8 .

Question

The maximum value of the function $f(x)=2 x^3-15 x^2+36 x-48$ on the set $A=\left\{x \mid x^2+20 \leq 9 x\right\}$ is, $(4,-1)$, 8 .

Answer 1

SOLUTION : $A=\left\{x \mid x^2+20 \leq 9 x\right\}=\{x \mid x \in[4,5]\}$

Now, $f^{\prime}(x)=6\left(x^2-5 x+6\right)$

$f^{\prime}(x)=0 \Rightarrow \quad x=2,3$

$f(2)=-20, f(3)=-21, f(4)=-16, f(5)=7$

from graph, maximum of $f(x)$ on set $A$ is $f(5)=7$