The curve satisfies $\frac{dy}{dx} = \sqrt{4x + 1}$, and the point $(2, 5)$ lies on it.
(i)[4]
Find the curve's equation.
(ii)[2]
Point $P$ travels along the curve so that its $y$-coordinate is rising at a steady rate of $0.06$ units per second. Determine the rate of change of the $x$-coordinate when $P$ is at $(2, 5)$.
(iii)[2]
Show that $\frac{d^2 y}{dx^2} \times \frac{dy}{dx}$ has a constant value.
Worked solution & mark scheme
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