3.16: Stationary point involving surds

0606/12/M/J/21 — Question 6 · 7 marks

Do not use a calculator in this question.

A curve has equation y=3x2+5x85x+60y = 3x^{2} + 5x - 8\sqrt{5x} + 60.
(a)
Find the xx-coordinate of the stationary point on the curve, giving your answer in the form a+b5a + b\sqrt{5}, where aa and bb are integers.
[4]
(b)
Hence find the yy-coordinate of this stationary point, giving your answer in the form c5c\sqrt{5}, where cc is an integer.
[3]