The largest value of a logarithmic quotient

The largest value of a logarithmic quotient

Secondary 4
6 marks
TGM Original Questions

A curve has equation \(y=\frac{\ln x+2}{x}\), where \(x>0\).

  1. Find \(\frac{\mathrm{d}y}{\mathrm{d}x}\).[2]
  2. Find the exact coordinates of the stationary point and determine its nature.[4]

Solution:

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Answer:(a) \(-\frac{\ln x+1}{x^2}\). (b) Maximum at \((e^{-1},e)\).

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