At what points, the slope of the curve `y=-x^2+3x^2+9x-27` is maximum? Also, find the maximum slope.

Explanation

Given, curve `y=-x^{3}+3 x^{2}+9 x-27`


Differentiating both sides w.r.t. x, we get


`d y / d x=-3 x^{2}+6 x+9`


Let slope of the curve `d y / d x=z`


So, `z=-3 x^{2}+6 x+9`


Differentiating both sides w.r.t. x, we get


`d z / d x=-6 x+6`


For local maxima and local minima,


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