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5-103.

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

  1. 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.

  2. 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?

  3. 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?

  4. 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.
Click the link at right for the full version of the eTool: Calc 5-103 HW eTool