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3-188.

ANOTHER PROBLEM FOR HANAH

  1. Graph on graph paper. Then without a calculator, sketch on the same set of axes.

  2. Describe the graphs of and at .

  3. Use your graphing calculator to determine the slope of at the vertex.

    Though the derivative does not exist, some graphing calculators (inaccurately) say that the derivative is at a cusp.

  4. Calculators are not always accurate. Some graphing calculators incorrectly determine slopes at a vertex, as well as other cusps, because they use the symmetric difference quotient to calculate the slope of a tangent line.

    For , use , to calculate for and . What do you notice? What leads a calculator to give a false derivative of  at ?

Compute without a calculator