The equation of the curve is $y = \mathrm{f}(x)$, where $\mathrm{f}(x) = (x+4)\sqrt{2x-3}$,

Question

The equation of the curve is $y = \mathrm{f}(x)$, where $\mathrm{f}(x) = (x+4)\sqrt{2x-3}$, $x > \frac{3}{2}$. Show that $\mathrm{f}'(x) = \frac{px+q}{\sqrt{2x-3}}$, where $p$ and $q$ are integers.[3] Find the $x$-coordinates of the points where the gradient of the normal of $-\frac{1}{7}$.[5] Determine whether $\mathrm{f}$ is an increasing or decreasing function. Explain your answer.[2]

Accepted Answer

(a)p = 3, q = 1 (b)x-coordinates =$\frac{74}{9} $ or x = 2

2025 MGS PRELIMS P2 Q8

2025 MGS PRELIMS P2 Q8