Find $f'(x)$ .

The graph of $f$ has a gradient of $3$ at the point P. Find the value of $a$ .

$f'(x) = 3a{x^2} - 12x$     A1A1     N2

Note: Award A1 for each correct term.

[2 marks]

setting their derivative equal to 3 (seen anywhere)     A1

e.g. $f'(x) = 3$

attempt to substitute $x = 1$ into $f'(x)$     (M1)

e.g. $3a{(1)^2} - 12(1)$

correct substitution into $f'(x)$     (A1)

e.g. $3a - 12$ , $3a = 15$

$a = 5$    A1     N2

[4 marks]

A majority of candidates answered part (a) correctly, and a good number earned full marks on both parts of this question. In part (b), some common errors included setting the derivative equal to zero, or substituting 3 for x in their derivative. There were also a few candidates who incorrectly tried to work with $f(x)$ , rather than $f'(x)$ , in part (b).

A majority of candidates answered part (a) correctly, and a good number earned full marks on both parts of this question. In part (b), some common errors included setting the derivative equal to zero, or substituting $3$ for $x$ in their derivative. There were also a few candidates who incorrectly tried to work with $f(x)$ , rather than $f'(x)$ , in part (b).