### Home > APCALC > Chapter 4 > Lesson 4.3.1 > Problem 4-114

4-114.

Differentiate the following functions. Determine if each function is differentiable for all real values of .

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

ThenThe 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?