textbook-theory · English
Difference Equations to Differential Equations — Section 3.8: Finding Maximum and Minimum Values
Section 3.8 of Dan Sloughter's open calculus textbook covers techniques for finding maximum and minimum values of continuous functions on both closed and open intervals. The section introduces critical points, singular points, the first derivative test, and the second derivative test for local extrema, illustrated with worked examples including trigonometric optimization, maximum likelihood estimation, and a cylindrical can surface-area minimization problem. A problem set of 22 exercises reinforces these techniques.
optimizationcalculusdifferential calculusextrema