MATH 265 Study Guide - Midterm Guide: Minimax, Universal Windows Platform Apps, Asteroid Family

• School: University of Calgary
• Department: Mathematics
• Course: MATH 265
• Professor: Michael Cavers

Document Summary

Absolute (or global) max f(x)<= f(c) and min f(x)>= f(c) Local (or relative) max f(x)<= f(c) and min f(x)>= f(c) for open interval (window) The extreme value theorem (evt) (both max & min) If continuous on closed interval: must attain abs max and min. If not continuous: evt not always hold. Critical point (number or value) if: c is in the domain (meaning open circle is not in domain) 2. either f"(c) =0 or undefined. Other textbook calls it singular points, or endpoints. Example: root x f"(x) are not zero: but f"(x) is undefined if x=0 (& x< o but not in domain) so it is a critical point. Max & min continued: critical is tool to find max/min points. If f(x) has local max or min at x=c, then x=c is either a critical point or is on endpoint of interval. Note critical pt does not be a local max/min.