Find the absolute maximum and absolute mininimum values,if any, of the fuction. g(x) = cosx - sinx on [0,2π]  

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Here is a graph of g(x):The endpoints x=0 and x=2π are obviously not an absolute max or min.  From looking at the graph it appears x=3π/4 is a min and 7π/4 is the max.Confirm by taking the first derivative and setting equal to zero.  Solve for x.Hope that helps