Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve is defined by $y = f(x)$, and you are told that $f'(x) = ax^2 + bx$, with $a$ and $b$ positive constants.
(i)[3]

Find, in terms of $a$ and $b$, the non-zero value of $x$ at which the curve has a stationary point and determine, showing all necessary working, the type of stationary point.

(ii)[6]

You are now told that the curve has a stationary point at $(-2, -3)$ and that the gradient of the curve at $x = 1$ is $9$. Find $f(x)$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Identifies stationary point $x=-\frac{b}{a}$” …

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI