Consider the function $f(x) = a{x^2} + c$.

Find $f'(x)$

Point ${\text{A}}( - 2,\,5)$  lies on the graph of $y = f(x)$ . The gradient of the tangent to this graph at ${\text{A}}$ is $- 6$ .

Find the value of $a$ .

Find the value of $c$ .

$2ax$      (A1)   (C1)

Note: Award (A1) for $2ax$.  Award (A0) if other terms are seen.

$2a( - 2) =  - 6$       (M1)(M1)

Note: Award (M1) for correct substitution of $x =  - 2$  in their gradient function, (M1) for equating their gradient function to $- 6$ . Follow through from part (a).

$(a = )1.5\,\,\,\left( {\frac{3}{2}} \right)$       (A1)(ft) (C3)

${\text{their }}1.5 \times {( - 2)^2} + c = 5$         (M1)

Note: Award (M1) for correct substitution of their $a$ and point ${\text{A}}$. Follow through from part (b).

$(c = ) - 1$         (A1)(ft) (C2)

Question 11: Equation of tangent
Part (a) was generally well answered.

In part (b), many candidates substituted the value of the function, rather than its gradient; this was usually correctly followed through into part (c).

In part (b), many candidates substituted the value of the function, rather than its gradient; this was usually correctly followed through into part (c).