At what points, the slope of the curve `y=-x^3+3x^2+9x-27` at point `(x ,\ \ y)` is given by maximum slope.

Explanation

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



`frac{{dy}}{prime} d x=-3 {x}^{2}+6 {x}+9`



`therefore` Slope of the given curve,



`m=-3 x^{2}+6 x+9 quad ldots(frac{d y}{d x}=m)`



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