The curve is given by $y = x^3 + px^2$, where $p$ is a positive constant. A second curve is given by $y = x^3 + px^2 + px$.
(i)[4]
Show that the origin is a stationary point on the curve $y = x^3 + px^2$ and determine the coordinates, in terms of $p$, of the remaining stationary point.
(ii)[3]
Determine the type of each stationary point.
(iii)[3]
Find the range of values of $p$ for which the curve $y = x^3 + px^2 + px$ has no stationary points.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$\dfrac{dy}{dx}=3x^2+2px$” …