Example 2.  Graph  [Graphics:Images/NumericalDiffMod_gr_67.gif].  Find the bound  [Graphics:Images/NumericalDiffMod_gr_68.gif].  Look at a graph and estimate the value  [Graphics:Images/NumericalDiffMod_gr_69.gif], be sure to take the absolute value if necessary.

Solution 2.

[Graphics:../Images/NumericalDiffMod_gr_70.gif]

[Graphics:../Images/NumericalDiffMod_gr_71.gif]

[Graphics:../Images/NumericalDiffMod_gr_72.gif]

The maximum occurs at x = 0 and the minimum occurs at [Graphics:../Images/NumericalDiffMod_gr_73.gif] .  Now find the formula for the error bound.

[Graphics:../Images/NumericalDiffMod_gr_74.gif]
[Graphics:../Images/NumericalDiffMod_gr_75.gif] [Graphics:../Images/NumericalDiffMod_gr_76.gif] [Graphics:../Images/NumericalDiffMod_gr_77.gif] [Graphics:../Images/NumericalDiffMod_gr_78.gif] [Graphics:../Images/NumericalDiffMod_gr_79.gif] [Graphics:../Images/NumericalDiffMod_gr_80.gif]

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003