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To calculate the slope of a line tangent to at , most graphing calculators use Hanah’s method from problem 3-35, formally called the symmetric difference quotient, shown below.

  1. Use the symmetric difference quotient to determine if .

    Expand the numerator.
    Combine like terms.
    Factor out an .
    Cancel out the .
    Evaluate the limit .... this is .

  2. Use this symmetric difference in your graphing calculator to graph for for .

    Graph that on your calculator. Also sketch the derivative function you found in part (a). The sketches should look a lot alike.