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In Chapter 4, it was discovered that was not differentiable at .

  1. Why does the derivative of not exist at ?

    What is the slope of the function at this point? Can you compute it?

  2. Is differentiable at ? Why or why not?

    Graph the function or evaluate the derivative at .

    No, the tangent is still vertical (and in this case there is a cusp).

  3. What about ?

    Simplify .

  4. Explain why there is a point of inflection at for .

    What happens on either side of a point of inflection?What kind of change does a point of inflection signify?

    Even though DNE, there is still a point of inflection because the graph changes from concave up to concave down at .