MATH 140 Lecture 25: Symmetry
6 Nov 2015
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The graph of f is never symmetric with respect to the x axis unless f ( x)=0 for all x in the domain: symmetry with respect to the origin. f ( x)= f (x ) 1. f ( x)=x4 2x2+2 f " ( x)=4 x3 4x=4 (x2 1)=4( x+1)( x 1) f " "( x)=12 x2 4 f " (x)=0if x=0 x= 1 f " " (x)=0if x= 1. 3 f " " ( 1)>0 f ( 1)=1=rel. min. f " " (1)>0 f (1)=1=rel min f " " (0)<0 f " "( 0)=2=rel max o o o o o: the graph of f is concave upward on downward on ( 1. , 13 and f ( x)=f ( x) symmetry about y axis o: graph, note: if f has only even power of x in its equation, then the graph is symmetric with respect to the y axis.
