Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve is given by the parametric equations $x = \ln (t + 1)$ and $y = t^2 \ln t$.

(i)[5]

Find an expression, in terms of $t$, for $\frac{dy}{dx}$.

(ii)[2]

Find the exact value of $t$ for the stationary point.

(iii)[2]

Find the gradient of the curve at the point where it meets the $x$-axis.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State that $\dfrac{dx}{dt} = \dfrac{1}{t+1}$” …