CPM Homework Banner

Consider the curve .

  1. Find .

    Implicitly differentiate.

  2. Find the equation of the tangent line at .

    Notice that the derivative you found in part (a) has both - and -values.

  3. If , estimate using the tangent line.

    Since is easier to evaluate in a linear equation than in the curve shown above, use the tangent line to estimate the -value at .

  4. Using , determine if the tangent approximation is an over or under estimate. Justify your answer in words.

    When finding , remember to substitute your answer in part (a).

    The sign of the 2nd derivative at will determine if the tangent line is above or below the curve.

    When a function is concave up, the tangent line will be below the curve.
    When it is concave down, the tangent line will be above the curve.
    Verify these statements by sketching a few examples.