Level 3 Differentiation Walkthrough

Question 1(d)

2022 Paper - Parametric differentiation

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Question

A curve is defined parametrically by the equations:

\[ x=2+3t \qquad \text{and} \qquad y=3t-\ln(3t-1), \qquad t>\frac{1}{3} \]

Find the coordinates, \((x,y)\), of any point(s) on the curve where the tangent to the curve has a gradient of \(\frac{1}{2}\).

Try the question yourself first. If you get stuck, open the hints before using the full walkthrough.

You must use calculus and show any derivatives that you need.