Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve is given by $y = 2x^{\frac{1}{2}} - 1$.
(a)[3]

Find the equation of the normal to the curve at the point $A\,(4, 3)$, and give your answer in the form $y = mx + c$.

(b)[2]

Find the rate at which the $y$-coordinate is increasing at $A$.

(c)[3]

As the point moves down the normal, determine the rate at which its $x$-coordinate changes.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct differentiation gives gradient $m=\frac12$ when $x=4$” …

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