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 \(y = mx + c\) .