The curve is defined by $y = x^3 + x^2 - x$. One stationary point occurs at $\left(\dfrac{1}{3}, -\dfrac{5}{27}\right)$.
(a)[5]
State the coordinates of the remaining stationary point.
(b)[2]
Use a sketch of the graph of $y = x^3 + x^2 - x$ to decide whether the stationary point $\left(\dfrac{1}{3}, -\dfrac{5}{27}\right)$ is a maximum or a minimum.
(c)[2]
Find the set of possible values of $k$ for which the equation $x^3 + x^2 - x = k$ has fewer than 3 solutions.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The stationary point is $(-1,1)$.” …