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You have f(x). You find f’(x). You discover that f’(3) DNE. Does that mean there’s a discontinuity in the graph of f(x) at that point? Explain.
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no, it means that there is either a discontinuity so that f(3) DNE, or a cusp so that f'(3) DNE. (Think of f(x)=|x-3|)
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