Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

A curve is defined by the equation $y = k(3x - k)^{-1} + 3x$, with $k$ taken as a constant.
(a)[4]

In terms of $k$, determine the $x$-coordinates where a stationary point occurs.

(b)[3]

The function $f$ has a stationary value at $x = a$ and is given by $f(x) = 4(3x - 4)^{-1} + 3x$ for $x \geq \frac{3}{2}$. Find $a$ and decide what type of stationary value it is.

(c)[2]

The function $g$ is given by $g(x) = -(3x + 1)^{-1} + 3x$ for $x \geq 0$. State, with clear reasoning, whether $g$ is increasing, decreasing or neither.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: On differentiation, $\frac{dy}{dx}=-k(3x-k)^{-2}(3)$

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