The slope of the function $f(x)=-\frac{x^3}{3}+\frac{5x^2}{2}-6x+12 $ is maximum at x= __________.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{5}{2}$
$f(x)=-\frac{x^3}{3}+\frac{5x^2}{2}-6x+12$
Slope = $f'(x)$
$=-x^2+5x-6$
and, thus critical points is,
$f''(c)=0$
$⇒-2x+5=0$
$⇒x=\frac{5}{2}$