### Home > APCALC > Chapter 5 > Lesson 5.2.5 > Problem 5-103

FUNKY FUNCTIONS REVISITED 5-103 HW eTool (Desmos). Homework Help ✎

Graph

*f*(*x*) =and rewrite *f*as a piecewise-defined function.There will be two pieces. The graph indicates that

*x*= −0.5 is the boundary point.Zoom in at

*x*= –0.5 on your graphing calculator and carefully examine the curve. Does*f*appear differentiable at*x*= –0.5? Why or why not?Does the slope from the left of

*x*= −0.5 appear to agree with the slope from the right?To confirm whether or not

*f*(*x*) =is differentiable at *x*= –0.5, examine*f*′. Use the piecewise-defined function from part (a) to write an equation for*f*′(for*x*≠ −0.5).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

*f*'(−0.5) from the left agrees with*f*'(−0.5) from the right.

Looking at the graphs, do the slopes appear to agree from both sides of −0.5?

Use the eTool below to help solve the problem.

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