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

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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.