1. Find the exact absolute maximum and absolute minimum values of f(x) = 2cosx+ sin(2x) on the interval [0, ~ ]. f(x) = 2cosx + sin(2x) f'(x) =-2sin x+ 2cos(2x) 0 = -2sin x + 2(1 -2sin x) 0 = -2sin x + 2-4sin x 2 sin x + sinx-1=0 (2 sin x -1)(sin x +1) = 0 sin x = - or sin x = -1 2 3TT x = sin x =- 2 f(0) =2 f sin| =2.59807 ( 2) =0 The absolute maximum value is 2.59807 that occurs at x = sin The absolute minimum value is 0 that occurs at x =- 3 TT 2