### Home > CALC3RD > Chapter Ch5 > Lesson 5.2.5 > Problem 5-103

Graph

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. Doesappear 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?Does

? Justify your answer. Notice Hana's definition of the derivative! This question is asking

from the left agrees withfrom 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*