Find the maximum slope of the curve `y=-x^3+3x^2+2x-27` .

Explanation

Equation of the given curve is:

y = – `x_3` + `3x^2` + 9x – 27

Differentiating on both sides, we get;

`(dy)/(dx)` = y’ = – `3x^2` + 6x + 9

This equation represents the slope of the curve.

Now differentiating dy/dx, we get;

`(d^2y)/(dx^2)` = – 6x + 6 = – 6 (x – 1)

Let us consider,`(d^2y) / (dx^2)` = 0
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