(a)[4]
Show that it follows that $\dfrac{dy}{dx} = \dfrac{4\ln t - 2}{\sqrt{t}}$.
(b)[2]
Find the exact gradient at $B$ on the curve.
(c)[3]
Find M's exact coordinates.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The diagram represents the curve with parametric equations $x = 1 + \sqrt{t}$, $y = (\ln t + 2)(\ln t - 3)$, for $0 \le t \le 25$. It meets the $x$-axis at the points $A$ and $B$ and has a minimum point $M$.