Learning Guide Learning Guide

214 • Chapter 6: Examples from Calculus0.16022xi44xTo find the size of the error, you need a full analysis of the expressionerr for x between 2 and 4 and ξ between a and x, that is, on the twoclosed regions bounded by x = 2, x = 4, ξ = a, and ξ = x. The curvecommand from the plottools package can illustrate these two regions.> with(plots): with(plottools):Warning, the name changecoords has been redefinedWarning, the name arrow has been redefined> display( curve( [ [2,2], [2,a], [4,a], [4,4], [2,2] ] ),> labels=[x, xi] );43.5xi32.522 2.5 3 3.5 4xThe partial derivatives of err help you find extrema of err inside thetwo regions. Then you need to check the four boundaries. The two partialderivatives of err are> err_x := diff(err, x);