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:
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?