The curve $C$ has equation $y = \frac{1}{4x - x^2}$. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$. H

Question

The curve $C$ has equation $y = \frac{1}{4x - x^2}$. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$. Hence, find the $x$-coordinate, $x = x_1$, of the turning point on $C$ and determine its nature.[3] Using calculus, find the exact area of the region between $C$, the $x$-axis and the lines with equations $x = 1$ and $x = x_1$.[3]

Accepted Answer

(a) $\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x-4}{(4x-x^2)^2}$, with a minimum at $x=2$ (b) $\dfrac14\ln3\text{ units}^2$

2025 JPJC P1 Q1

2025 JPJC P1 Q1

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