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CalculusChallengeThe Derivative

The Derivative · Challenge problem

A function is defined by f(x)=x2f(x)=x^2 for x≤1x\le1 and f(x)=ax+bf(x)=ax+b for x>1x>1. Find the value of a⋅ba\cdot b that makes ff DIFFERENTIABLE at x=1x=1 (not just continuous there).