MATH 154 Lecture Notes - Lecture 18: Maxima And Minima

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 154
• Professor: Yusuf Tuncer

Document Summary

A function f(x) has a local minimum at a point if the value of f at that point is smaller than the value of f at all nearby points. A function f(x) has a local maximum at a point if the value of f at that point is larger than the value of f at all nearby points. At a local maximum or minimum, the slope of f" is 0. At a local maximum, the slope of f" changes from + to . At a local minimum, the slope of f" changes from to + Note: the quadratic does not give a real root, so the only root we can use is x = 0 if we use f(x) So f(x) is continuously increasing, with no maximums or minimums. The sign pattern of f"" tells us where f" is increasing or decreasing (concavity of f) F(x) is concave up when f""(x) is greater than 0.