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:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 50
$f(x)=x^3-9x^2+33x+5$
$f'(x)=3x^2-18x+33$
$\text{Least rate of increase} \Rightarrow \text{minimum of } f'(x)$
$f''(x)=6x-18$
$6x-18=0 \Rightarrow x=3$
$f(3)=27-81+99+5=50$
$\text{Required value} = 50$