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Consider the function .

  1. Write the equation of the line tangent to at .

    Evaluate to find the slope, and evaluate to find the -intercept. Use the point-slope formula to create the equation of the tangent line.

  2. Approximate using your answer to part (a).

    Use the tangent line at to evaluate . This will approximate . Why approximate?
    Since a tangent is a linear equation, it is easier to evaluate than .

  3. Is your approximation an underestimate or an overestimate of the actual value? Explain.

    A concave up graph has tangent lines that are below the curve. Sketch it, you will see.
    And a concave down graph has tangent lines that are above the curve.

    Overestimate since