1.55: Normal to a logarithmic quotient

0606/12/O/N/20 — Question 7 · 7 marks

A curve has equation y=ln⁡(3x2−5)2x+1y = \dfrac{\ln(3x^{2} - 5)}{2x + 1} for 3x2>53x^{2} > 5.
(a)
Find the equation of the normal to the curve at the point where x=2x = \sqrt{2}.
[6]
(b)
Find the approximate change in yy as xx increases from 2\sqrt{2} to 2+h\sqrt{2} + h, where hh is small.
[1]