The value of the function $f(x)=x^3-9 x^2+33 x+5, x \in R$, where its rate of increase is least, is:

50

The correct answer is Option (3) → 50

$f(x)=x^3-9x^2+33x+5$

$f'(x)=3x^2-18x+33$

$\text{Least rate of increase} \Rightarrow \text{minimum of } f'(x)$

$f''(x)=6x-18$

$6x-18=0 \Rightarrow x=3$

$f(3)=27-81+99+5=50$

$\text{Required value} = 50$