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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?