3.109: Stationary points and sketch of a cubic product

0606/12/F/M/23 — Question 2 · 10 marks

A curve has equation y=(x+2)2(5−x)y = (x + 2)^{2}(5 - x).
(a)
Find the xx-coordinates of the stationary points on the curve.
[4]
(b)
On the axes, sketch the graph of y=(x+2)2(5−x)y = (x + 2)^{2}(5 - x), stating the coordinates of the points where the curve meets the axes.
[3]
(c)
Find the values of kk for which the equation k=(x+2)2(5−x)k = (x + 2)^{2}(5 - x) has one distinct root only.
[3]