[SOLVED] Sketching the Curves of a Function W/In an Interval - Simple (1st Year Calcu 1. The problem statement, all variables and given/known data Sketch the graph of the function on the interval [0, 2pi]. y = cosx - 1/2(cos2x) 2. Relevant equations 3. The attempt at a solution so the problems that i have been practicing like this have been pretty simple. i determine all of the following: domain and range x and y intercepts whether or not there is discontinuity whether or not there is symmetry intervals of increasing and decreasing order extrema points of inflection concavity whether or not there exist asymptotes the problem is that mathematically i located a single extreme value at (pi, -3/2), but graphically, there appears to be more. http://img149.imageshack.us/img149/1645/graphscreenshotth2.th.png [Broken] is not each change in direction a relative minimum/maximum value? i can only seem to locate the absolute minimum value within the interval, but none of the other relative extreme values. any idea as to where i am going wrong? so, the first derivative of the given function is -sinx + sin2x. solving this equation is where i find possible extrema at 0, pi, and 2pi. any ideas why i can't seem to locate the other extrema algebraically?