Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

A curve has equation $y = kx^{\frac{1}{2}} - 4x^2 + 2$, with $k$ denoting a constant.
(a)[2]

Find $\frac{dy}{dx}$ and $\frac{d^2y}{dx^2}$ in terms of $k$.

(b)[4]

It is given that $k = 2$. Find the coordinates of the stationary point and determine whether it is a maximum or minimum.

(c)[6]

The points $A$ and $B$ on the curve have $x$-coordinates $0.25$ and $1$ respectively. For another value of $k$, the tangents to the curve at $A$ and $B$ intersect at a point whose $x$-coordinate is $0.6$. Find this value of $k$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Obtaining $\frac{dy}{dx}=\frac12kx^{-\frac12}-8x$.

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