3.1.8 Making a Function Differentiable - Analytic Geometry and Calculus I

In this video, we solve problem 115 from section 2.2 of the Larson Calculus text, 10th edition.
We're given a piecewise function containing parameters an and b, and were asked to select an and b so that the resulting function is differentiable for all x-values. This involves selecting a and b so that the limit of the function from the left and right, as x approaches any discontinuity, match, and so that the derivatives of the function from the left and right at each point of (potential) discontinuity are equal. If the limits are equal, and the derivatives are equal at every x-value, the resulting function will have a well-defined derivative everywhere.
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