MatrixMathematics I

Continuity and differentiability at a join

A function defined by two formulas that meet at x = c. Adjust a and b to make it continuous, then differentiable.

Figure 1.2.Drag a and b, or press a solve button. For continuity the left and right values at c must agree. For differentiability the left and right slopes must agree as well. Open on its own

Continuity at c gives one equation in a and b. Differentiability adds a second, from the derivatives of the two pieces.

A function can be continuous at c without being differentiable there, as at a corner.