Themaximum value of the finction $f(x)=3 x^{3}-18 x^{2}+27 x-40$ on the set $\mathrm{S}=\left\{x \in R:…
Themaximum value of the finction $f(x)=3 x^{3}-18 x^{2}+27 x-40$
on the set $\mathrm{S}=\left\{x \in R: x^{2}+30 \leq 11 x\right\}$ is :
-122
-222
122
222
Solution
Consider the function,
$f(x)=3 x(x-3)^{2}-40$
$\operatorname{Now} S=\left\{x \in \infty k: x^{2}+30 \leq 11 x\right\}$
So $x^{2}-11 x+30 \leq 0 \quad \Rightarrow \quad x \circ \in[5,6]$
$\therefore f(x)$ will have maximum value for $x=6$ The maximum value of function is,
$f(6)=3 \times 6 \times 3 \times 3-40=122$