Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

For the curve, the gradient at $(x, y)$ is $\frac{dy}{dx} = 2\sqrt{x + 3} - x$. It has a stationary point at $(a, 14)$, with $a$ a positive constant.
(a)[3]

Find $a$.

(b)[3]

Determine what type of stationary point it is.

(c)[4]

Find the curve's equation.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Sets $\frac{dy}{dx}=0$, leading to $2\sqrt{a+3}-a=0$” …

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