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Critical Points

"Define f(x) to be the distance from x to the nearest integer. What are the critical points of f."

Solution Preview

First, draw a graph of f(x):

When x is an integer, f(x) = 0 (and that's the minimum f(x) can be). The maximum f(x) can be is f(x) = 0.5 at x = 0.5, 1.5, 2.5, etc. (halfway between the integers). ...