Mathematics

Mathematics

Problem

A function mm is continuous for all real numbers and differentiable everywhere except at x=1x=1, where m′m' is undefined. The derivative satisfies m′(x)=3m'(x)=3 for x<1x<1 and m′(x)=−2m'(x)=-2 for x>1x>1. Determine whether mm attains a relative extremum at x=1x=1, and state whether the graph of mm has a sharp corner there.

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