Educational Materials

Derivative Signs

Ruth Dover

Author

Ruth Dover

Title

Derivative Signs

Description

Plots a function with colors to show where the first and second derivatives are positive and negative.

First derivative

This will plot the function red where the first derivative is positive and blue where the derivative is negative.

In[]:=

fder[x_]:=Evaluate[D[f[x],x]];Show[Plot[f[x],{x,xmin,xmax},RegionFunctionFunction[{x,y},fder[x]>0],PlotStyle{Red,Thick}],Plot[f[x],{x,xmin,xmax},RegionFunctionFunction[{x,y},fder[x]<0],PlotStyle{Blue,Thick}],PlotRangeAll]

Below, you will see the same colored graph along with the graph of the first derivative of ƒ shown in green.

In[]:=

Second derivative

This next command will plot the function green where the second derivative is positive and purple where the second derivative is negative.

In[]:=

secder[x_]:=Evaluate[D[f[x],{x,2}]];Show[Plot[f[x],{x,xmin,xmax},RegionFunctionFunction[{x,y},secder[x]>0],PlotStyle{Cyan,Thick}],Plot[f[x],{x,xmin,xmax},RegionFunctionFunction[{x,y},secder[x]<0],PlotStyle{Purple,Thick}],PlotRangeAll]

Below, you will see the same colored graph along with the graph of the second derivative of ƒ shown in blue.

In[]:=

Cite this as: Ruth Dover, "Derivative Signs" from the Notebook Archive (2019), https://notebookarchive.org/2018-12-bkof6n9