Average Rate of Change

Author

Eric W. Weisstein
January 24, 2017

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/AverageRateofChange.nb.

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

©2017 Wolfram Research, Inc. except for portions noted otherwise

Figure

f[x_]:=x+x^3+10

Plot[f[x],{x,-2,3},Epilog->{
Text[HoldForm[f[x]],{3,43}],
Text[A[x,a],{3.5,28}],
Text[Row[{"(",x,",",HoldForm[f[x]],")"}],{1,15}],
Text[Row[{"(",a,",",HoldForm[f[a]],")"}],{2.3,17}],
AbsolutePointSize[8],Red,Point[p={{1,f[1]},{2,f[2]}}],
AbsoluteDashing[5],InfiniteLine[p]
},
AxesLabel->{x,y},PlotRange->{{-2,3.8},{-1,45}}]

Derivative

f[x_]=.

Limit[((f[x]-f[a])/(x-a)),a->x,Analytic->True]