The original worked lessons remain the main explanations. Use these focused reminders to check the conditions before you start.
Increasing, decreasing and stationary points
Use signs of the first derivative and give complete coordinates.
Classify maxima and minima with a valid test.
Distinguish local and absolute extrema; include endpoint candidates.
Find stationary candidates from \(f^{\prime}(x)=0\), then use the original function for their ordinates. A + to − derivative sign change gives a maximum; − to + gives a minimum. At a stationary point, \(f^{\prime\prime}>0\) gives a minimum and \(f^{\prime\prime}<0\) a maximum; zero is inconclusive. Compare endpoints for absolute extrema on a closed interval. No classification of points of inflexion is required here.