Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The function $f$ is given by $f(x) = x^2 + \frac{k}{x} + 2$ for $x > 0$.

(a)[3]

Since the curve with equation $y = f(x)$ has a stationary point at $x = 2$, determine $k$.

(b)[2]

Determine the type of stationary point.

(c)[2]

As this is the curve’s only stationary point, find the range of $f$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate to get $f'(x)=2x-\dfrac{k}{x^2}$.” …