3.49: Stationary points, sketch and values of kk

0606/13/M/J/24 — Question 3 · 9 marks

(a)
Find the coordinates of the stationary points on the curve y=(2x+1)2(x−3)y = (2x + 1)^{2}(x - 3).
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(b)
On the axes, sketch the graph of y=(2x+1)2(x−3)y = (2x + 1)^{2}(x - 3), stating the intercepts with the axes.
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(c)
Write down the values of kk for which the equation (2x+1)2(x−3)=k(2x + 1)^{2}(x - 3) = k has exactly one solution.
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