3.20: Stationary points, sketch and unique kk-level

0606/13/O/N/23 — Question 6 · 10 marks

The polynomial q(x)q(x) is given by q(x)=−13(2x−1)(x+3)2q(x) = -\dfrac{1}{3}(2x - 1)(x + 3)^{2}.
(a)
Find the xx-coordinates of the stationary points on the curve y=q(x)y = q(x).
[4]
(b)
On the axes, sketch the graph of y=q(x)y = q(x) stating the intercepts with the coordinate axes.
[3]
(c)
Find the values of kk such that q(x)=kq(x) = k has exactly one solution.
[3]