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Home > CALC > Chapter 4 > Lesson 4.3.1 > Problem 4-103


Differentiate the following functions. Determine if the function is differentiable for all reals.

  1. Compare the graph of with its parent .

    looks just like . Their periods are the same. Their amplitudes are the same. Their maximum and minimum -values are the same. Their SLOPES are the same. The only difference is their horizontal locations.

    The slopes will shift with the graph:

  1. The derivative will be a piecewise function as well. Differentiate each piece separately.

    Consider the boundary point of the derivative. Examine the two pieces at . Is the derivative continuous?