(a)[4]
Show that $\frac{dy}{dx} = \frac{6}{2t + 3}$, using the given parametrisation.
(b)[2]
Find the gradient of the curve at point $A$.
(c)[2]
Find the gradient of the curve at point $B$.
Mathematics 9709 · AS & A Level · Differentiation
Differentiation — practice question
The diagram depicts the curve given by the parametric equations $x = \ln(2t + 3)$ and $y = \frac{2t - 3}{2t + 3}$. It meets the $y$-axis at $A$ and crosses the $x$-axis at $B$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain $\frac{dx}{dt}=\frac{2}{2t+3}$ from the equation for $x$.” …
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