The diagram displays a section of the curve given by the parametric equations $x = t^2 + 4t$, $y = t^3 - 3t^2$. It has a minimum at $M$ and meets the $x$-axis at $P$.
(i)[4]
Find the gradient of the curve at the point $P$.
(ii)[3]
Find the coordinates of the point $M$.
(iii)[4]
The gradient at the point corresponding to parameter $t$ is denoted by $m$. Show that $3t^2 - (2m + 6)t - 4m = 0$ and hence find the set of possible values of $m$ for points on the curve.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain an expression for $\frac{dy}{dx}$ with a quadratic numerator and a linear denominator” …