The value of x for which the slope of the curve $y =-x^3 +3x^2+ 9x - 27 $ is maximum, is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1
$y =-x^3 +3x^2+ 9x - 27 $
Slope $S=y'=-3x^2+6x+9$
so $S'=-6x+6=0$
$⇒x=1$
$S''=-6$
so $x=1$ (point of maxima)
so $S_{max}=S(1)=-3+6+9=12$
at $x=1$