and rewrite as a piecewise-defined function.
There will be two pieces. The graph indicates that
is the boundary point.
Zoom in at
on your graphing calculator and carefully examine the curve. Does appear differentiable at ? Why or why not?
Does the slope from the left of
appear to agree with the slope from the right?
To confirm whether or not
is differentiable at , examine . Use the piecewise-defined function from part (a) to write an equation for (for ).
Find the derivative of each piece of your piecewise function.
Then evaluate these limits. Do they agree?
? Justify your answer.
Notice Hana's definition of the derivative! This question is asking
from the left agrees with from the right.
Looking at the graphs, do the slopes appear to agree from both sides of
Use the eTool below to help solve the problem.
Click the link at right for the full version of the eTool: Calc 5-103 HW eTool