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7-31.
  1. Consider the curve xe5y = 3y. Homework Help ✎

    1. Find .

    2. Find the equation of the tangent line at (0, 0).

    3. If x = 0.1, estimate y using the tangent line.

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

Implicitly differentiate.

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

Since x = 0.1 is easier to evaluate in a linear equation than in the curve shown above, use the tangent line to estimate the y-value at x = 0.1.

The sign of the 2nd derivative at (0,0) will determineif 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.