Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The function $f$ takes the form $f(x) = \frac{1}{x+1} + \frac{1}{(x+1)^2}$ for $x > -1$.
(i)[3]

Find $f'(x)$ for this function.

(ii)[1]

State, with a reason, whether $f$ is increasing, decreasing or neither.

(iii)[4]

The function $g$ takes the form $g(x) = \frac{1}{x+1} + \frac{1}{(x+1)^2}$ for $x < -1$. Find the coordinates of the stationary point on the curve $y = g(x)$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Attempt at differentiating $(x+1)^{-2}$

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