MATH 111 Lecture Notes - Lecture 19: Notation3, Maxima And Minima

• School: Emory University
• Department: Mathematics
• Course: MATH 111
• Professor: Huanhuan Yang

Document Summary

1476- lecture 19 - how derivatives affect the shape of a graph and optimization. Find extreme values through the change in sign of f . Show where the slope of f is increasing/decreasing. If the graph of f is above all of its tangents on an interval i, then it is concave upward. If the graph of f is below all of its tangents on an interval i, then it is concave downward. If f "(x) > 0 for all x in i, then the graph of f is concave upward on i. If f "(x) < 0 for all x in i, then the graph of f is concave downward on i. An inflection point is a point where the graph of f changes concavities. Like how extreme values are marked by f (x)= 0 or not existing, inflection points are marked by f "(x)= 0. Given that f " (x) is continuous near c.