Worked examples

Curve sketching and optimization

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Relative maxima and minima with the first derivative
• 2Concavity and inflection points
• 3Complete studies of rational functions
• 4Complete studies of exponential functions
• 5Complete studies of logarithmic functions
• 6Absolute maxima and minima on closed intervals
• 7Geometric optimization problems
• 8Maximum profit, minimum average cost and maximum revenue