Correct Answer - Option 2 : 12
Concept:
Slope m of the curve is given by dy/dx = 0
And, condition for slope to be maximum: d2y/dx2 = 0
(dy/dx)x = a gives the value of maximum slope.
Calculation:
y = – x3 + 3x2 + 9x – 27
dy/dx = – 3x2 + 6x + 9 = slope of the curve
Now, double differentiation:
d2y/dx2 = – 6x + 6 = – 6 (x – 1)
d2y/dx2 = 0
⇒ – 6 (x – 1) = 0
⇒ x = 1
clearly, d3y/dx3 = – 6 < 0 for all value of x
∴ The slope is maximum when x = 1.
(dy/dx)x = 1 = – 3 (1)2 + 6 × 1 + 9 = 12
