Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve is defined by $y = \frac{8}{\sqrt{x}} - 2x$.
(i)[3]

Find the coordinates of the stationary point on this curve.

(ii)[2]

Find an expression for $\frac{d^2y}{dx^2}$ and hence, or otherwise, determine the nature of the stationary point.

(iii)[3]

Find the values of $x$ for which the line $y = 6$ intersects the curve.

(iv)[1]

State the set of values of $k$ for which the line $y = k$ does not meet the curve.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Differentiates to get $\frac{dy}{dx}=4x^{\frac{1}{2}}-2$

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