Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The function $f$ is given by $f(x) = \frac{5}{1 - 3x}$, where $x \geq 1$.

(i)[2]

Find a formula for $f'(x)$.

(ii)[1]

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

(iii)[5]

Find a formula for $f^{-1}(x)$, and state both the domain and the range of $f^{-1}$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correctly differentiates $f(x)=\frac{5}{1-3x}$” …