Two stationary values of a logarithmic quotient

Two stationary values of a logarithmic quotient

Secondary 4
9 marks
TGM Original Questions

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

  1. Show that \(\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{\ln x(2-\ln x)}{x^2}\).[3]
  2. Find the exact coordinates of both stationary points and determine the nature of each.[4]
  3. State all intervals on which the function is decreasing.[2]

Solution:

Solution locked

Sign in to view the step-by-step solution

Similar questions are unavailable for this question.
Answer:(b) Minimum \((1,0)\); maximum \(\left(e^2,\frac4{e^2}\right)\). (c) \(0<x<1\) or \(x>e^2\).

Need help? Join our JC Math tuition classes.

Learn more