For the curve, the parametric equations are $x = \frac{2t + 1}{3t + 4}$ and $y = 2\ln(3t + 4)$, with $t > -\frac{4}{3}$.
(a)[5]
Show that $\frac{dy}{dx}$ may be written in the form $c(3t + 4)$, and give the value of the constant $c$.
(b)[4]
The gradient of the curve at the point $(a, \ln 100)$ is $m$. Determine $a$ and $m$.
(c)[1]
State whether the curve is decreasing, increasing, or neither, and explain your answer.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use of quotient rule (or equivalent) attempted for the derivative of $x$” …