(a)[3]
Find the rate at which the $y$-coordinate of $P$ is changing when $x = 9$. Give your answer in terms of the constant $a$.
(b)[2]
Find the value of $a$, given that the curve has a minimum point when $x = \frac{1}{4}$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
A point $P$ travels along the curve with equation $y = ax^{\frac{3}{2}} - 12x$ so that the $x$-coordinate of $P$ is increasing at a steady rate of 5 units per second.
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This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiates the expression to obtain $\frac{dy}{dx}=\tfrac32 ax^{\frac{1}{2}}-12$” …
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