3.5: Stationary points on a logarithmic–quadratic curve

0606/22/O/N/21 — Question 4 · 8 marks

A curve has equation y=3lnx+x27xy = 3\ln x + x^{2} - 7x, where x>0x > 0.
(a)
Find the xx-coordinates of the stationary points on the curve.
[5]
(b)
Determine the nature of each of these stationary points.
[3]