Maximum

Author

Eric W. Weisstein
November 23, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/Maximum.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Maximum.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Identities

Max[x,x]

Max[y,x]

Integrals

(∫_0^1)max(x,1-x)dx==(3/4)

PiecewiseExpand[Max[x,1-x],0<x<1]

Plot[Max[x,1-x],{x,0,1}]

Integrate[Max[x,1-x],{x,0,1}]

(∫_0^1)((min(x,1-x))/(max(x,1-x)))dx==2 ln(2)-1

PiecewiseExpand[((Min[x,1-x])/(Max[x,1-x])),0<x<1]

Plot[((Min[x,1-x])/(Max[x,1-x])),{x,0,1}]

Integrate[((Min[x,1-x])/(Max[x,1-x])),{x,0,1}]

(∫_0^1)((max(x,1-x))/(min(x,1-x)))dx==∞

PiecewiseExpand[((Max[x,1-x])/(Min[x,1-x])),0<x<1]

Plot[((Max[x,1-x])/(Min[x,1-x])),{x,0,1}]

Integrate[((Max[x,1-x])/(Min[x,1-x])),{x,0,1}]