The point $P$ lies on $$y=x^2-4x+1$$ and has $x$-coordinate $3$. Find: the coordinates of

Question

The point $P$ lies on $$y=x^2-4x+1$$ and has $x$-coordinate $3$. Find: the coordinates of $P$; the gradient of the curve at $P$; the equation of the tangent at $P$; the equation of the normal at $P$.

Accepted Answer

(a) $P=(3,-2)$; (b) Gradient $2$; (c) Tangent $y=2x-8$; (d) Normal $y=\frac{-x}{2-\frac{1}{2}}$.

Differentiation

Differentiation