MATH 1A Lecture Notes - Lecture 22: Farad, Asymptote, Antiderivative
Document Summary
Math 1a - lecture 22 - 4. 5 curve sketching and 4. 9 anti-derivatives. We can sketch a graph of y=f (x) by using: domain, special points, symmetry, asymptotes. Horizontal asymptotes: x x2 x2 x2 + 1 x2. =lim x lim x x x2 x2 x2 + 1 x2. = x2+1 2x2 (x2+1)2 = x2+1 (x2+1)2 f "( x)= . 0= x2+1 (this is the only thing that matters since the denominator is always positive) x= 1 f " ( x) So f ( x) increases on: local min: x= 1. U (1, ) and decreases on ( 1,1: concavity: f " " (x)= ( 2x) (x2+1)2 ( x2+1)(2(x2+1)2x) (x2+1)4 ( 2x)(x2+1) 4x(x2+1) (x2+1)3. 3
