(i)[4]
Show that $k = -2$ and then determine the $x$-coordinate of the other stationary point, $Q$.
(ii)[2]
Find $f''(x)$ and work out the nature of the stationary points $P$ and $Q$.
(iii)[4]
Find the function $f(x)$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The curve $y = f(x)$ passes through the stationary point $P(3, -10)$. It is also stated that $f'(x) = 2x^2 + kx - 12$, with $k$ as a constant.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate to get $f'(x)=18+3x-12$, then set this equal to zero” …
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