Calculus 1000A/B Quiz: Calculus 1000 - Assignment 3 Solution.pdf

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Geoff Wild

Document Summary

There are at least two ways to solve this problem, but each has to be thoroughly explained: let f(x) = | sin x cos x| = (cid:112)(sin x cos x)2. Since f(x) is periodic, it is enough to nd its absolute maximum on [0, 2 ]. Since f(x) is continuous on [0, 2 ], we can be sure that it attains an absolute maximum on [0, 2 ] by the extreme value theorem (page 275). We can nd the maximum by applying the closed. Given that x [0, 2 ], the rst equation is satis ed for x = /4 and x = 5 /4, and the second equation is satis ed when x = 3 /4 and x = 7 /4. Therefore the critical points are c = /4, 3 /4, 5 /4, 7 /4. If we now evaluate f at each critical point, and each endpoint we nd f(0) = f(2 ) = 1, f( /4) = 0,