Let be a polynomial curve.

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

Let

y=x^{3}-6x^{2}+9x+4

be a polynomial curve. (i) Show that

\dfrac{dy}{dx}=3x^{2}-12x+9

. (ii) Determine all points on the curve where the tangent is parallel to the

x

-axis. (iii) For each point obtained in part (ii), write the equation of the normal to the curve.