What is the largest value possible for the slope of the curve y=sin(x/2) support the answer

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nathanshields eNotes educator| Certified Educator

First, the slope of the curve is `d/(dx)sin(x/2)` right?  So we we want to find the maximum value of `1/2cos(x/2)` .   The cosine function oscillates between -1 and 1.  Since this function has been scaled by 1/2, the maximum value is 1/2.