Maximum slope of the curve y=-2x^3+6x^2+5x-20 is :

The correct answer is Option (3) → 11

The slope of the curve at any point is

    \( \displaystyle m = \frac{dy}{dx} = -6x^2 + 12x + 5 \)

At the maximum of the slope, the derivative of m is zero:

    \( \displaystyle \frac{dm}{dx} = -12x + 12 = 0 \)

    \(x = 1\)

    \( \displaystyle \frac{d^2m}{dx^2} = -12 \lt 0 \)

So the slope is greatest at x = 1:

    \(m(1) = -6 + 12 + 5 = 11\)