MATH 2250 Lecture Notes - Lecture 13: Maxima And Minima

• School: University of Georgia
• Department: Mathematics
• Course: MATH 2250
• Professor: Bergonio

Document Summary

Chapter 4a: extreme values of functions (this covers 4. 1 and 4. 3. ) We start this section with a few de nitions: De nition: given a function f , point x = c in its interior is called a critical point of f if f (c) is either equal to zero or is unde ned. Examples: for the following functions and their restricted domains, determine its maximum and minimum values, if they exist. Then compute the critical points of the functions on their interval: f (x) = x2 5 on [ 2, 2], h(x) = sin(x) on (0, ) This then leads us to a few theorems: for x 6= 0 for x = 0: g(x) = (cid:26) |x, j(x) = ex on ( , 0]. If f is continuous on a closed interval [a, b], then f attains both an absolute maximum value y = m and a minimum value y = m in [a, b].