4. The curve $$ y=x^{3}-6 x^{2}+9 x+3 $$ passes through the point $$ \mathrm{P}(2,5) $$ and has two turning points, $$ \mathrm{A}(3,3) $$ and B . Find a) the gradient of the curve at P . b) the equation of the normal to the curve at P . c) the coordinates of B and determine whether B is a maximum or the minimum point.

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a) The gradient at P is $$-3$$. b) The normal equation at P is $$ y = \frac{1}{3}x + \frac{13}{3} $$. c) B is at $$ (1, 7) $$ and is a maximum point.

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