MATH100 Study Guide - Final Guide: Apache Spark, Inflection Point

• School: University of Alberta
• Department: Mathematics
• Course: MATH100
• Professor: Ian Blokland

Document Summary

Polynomial example y=x4 2x2 ( higgs potential ) (1) domain:all x (2) y"=4 x3 4x y""=12x2 4 (3) critical points: y"=0 4x(x2 1)=0 4x( x+1)( x 1)=0 x=0 x= 1 x=1 (4) Local min (5) concavity y""=12x2 4=4 (3x2 1) y""=0 x2= 1. 3 y" " inflection point inflection point (6) no asymptotes (7) y 0 ( 1. Rational function example y= 2 x2+7 x+5 x+3 (1) domain: x 3 (6) vertical asymptote: y= 3. Oblique asymptote y =2x+1 (2) find y" y" " y"=2 2 ( x+3)2 y""= 4 ( x+3)3 (3) critical points y" d. n. eif x= 3 y""=0if x= 2 4 (4) 2 local min y""= +4 ( x+3)3 (5) Trigonometric example: y=x sin x ,[0,2 ] (1) domain: 0 x 2 (2) find y" y" " y"=1 cos x y""=+sin x (3) critical points: y"=0if cos x=1 x=0,2 (4)