Write down $\frac{{{\text{d}}y}}{{{\text{d}}x}}$.

The point ${\text{P}}(3{\text{, }}9)$ lies on the curve $y = {x^2}$ . Find the gradient of the tangent to the curve at P .

The point ${\text{P}}(3{\text{, }}9)$ lies on the curve $y = {x^2}$ . Find the equation of the normal to the curve at P . Give your answer in the form $y = mx + c$ .

$2x$     (A1)     (C1)

$2 \times 3$     (M1)
$= 6$     (A1)     (C2)

$m({\text{perp}}) =  - \frac{1}{6}$     (A1)(ft)

Note: Follow through from their answer to part (b).

Equation $(y - 9) =  - \frac{1}{6}(x - 3)$     (M1)

Note: Award (M1) for correct substitution in any formula for equation of a line.

$y =  - \frac{1}{6}x + 9\frac{1}{2}$     (A1)(ft)     (C3)

Note: Follow through from correct substitution of their gradient of the normal.
Note: There are no extra marks awarded for rearranging the equation to the form $y = mx + c$ .