Question

The maximum value of the function $f\left(x\right) = 3x^{8} - 18x^{2} + 27x - 40 $ on the set $S = \{ x \int R : x^2 + 30 \le 11 x \}$ is :

• A. 122
• B. -222
• C. -122
• D. 222

Answer 1

Answer: (A)

$S = \left\{x \in R, x^{2} +30 -11x\le0\right\} $
$ =\left\{x\in R , 5 \le x \le 6\right\}$
Now $ f\left(x\right) =3x^{3} -18x^{2} +27x-40$
$ \Rightarrow f'\left(x\right) =9\left(x-1\right)\left(x-3\right)$,
which is positive in $[5, 6]$
$ \Rightarrow \; f(x) $ increasing in $[5, 6]$
Hence maximum value = $f(6) = 122$