MAT135H1 Lecture Notes - Lecture 11: Asymptote, Even And Odd Functions, Maxima And Minima

• School: UTSG
• Department: Mathematics
• Course: MAT135H1
• Professor: natalia Christina Garcia

Document Summary

Mat135h1 f - lecture 11 - calculus 1(a) = 0 and does not use l"hopital"s rule; 0 divided by anything is 0, and anything divided by is 0, so answer is clearly defined without manipulation. Although x = 0 looks like a local minimum if graphed on a calculator, will find that it is actually a local maximum. Calculator cannot accurately determine behavior of critical point. Process of determining critical points: find domain and range, find x-intercepts and y-intercepts, look for symmetry (even or odd function) even: f x( ) = f x( odd: f x( ) = f x( ) (the same: asymptotes (horizontal, vertical, oblique / slant) vertical: denominator = 0 horizontal: approaches infinity oblique / slant: how the function approaches infinity. 5. use derivatives to find where function is increasing or decreasing: maximum and minimum, concavity. Definition: let f x( ) and g x( ) be continuous functions.