Learning Guide Learning Guide

6.1 Introductory Calculus • 217Two solutions to err_xi=0 seem to exist between 2 and 4 where solvefound none: π/2 is less than 2. Thus, you must use numerical methods. Ifx = 2, then ξ should be in the interval from 2 to a.> sol := fsolve( eval(err_xi, x=2), xi, 2..a );sol := 2.446729125At that point the error is> eval( err, {x=2, xi=sol});0.07333000221 (2 − π) 6Now add this value to the set of critical values.> critical := critical union {%};critical := {0, 0.07333000221 (2 − π) 6 }If x = 4 then ξ should be between a and 4.> sol := fsolve( eval(err_xi, x=4), xi, a..4 );sol := 3.467295314At that point, the error is> eval( err, {x=4, xi=sol} );−0.01542298119 (4 − π) 6> critical := critical union {%};critical :={0, −0.01542298119 (4 − π) 6 , 0.07333000221 (2 − π) 6 }At the ξ = a boundary, the error is> B := eval( err, xi=a );B := − 1 (x − π)6240