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

4-103.

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

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:

If

Then

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?