At what point, the slope of the curve y = – x3 + 3×2 + 9x – 27 is maximum? Also find the maximum slope.

Given, CURVE

   

Separating the two sides w.r.t. x, we get

   

Let SLOPE of the CURVE

   

Thus,

   

Separating the two sides w.r.t. x, we get

   

For LOCAL maxima and nearby minima,

   

   

   

Putting

   

in condition of the CURVE

   

   

Most extreme SLOPE

   

Accordingly, (1, – 16) is where the SLOPE of the given CURVE is greatest and most extreme incline =