### Home > CALC > Chapter 7 > Lesson 7.1.3 > Problem 7-31

Consider the curve

Find

. Implicitly differentiate.

Find the equation of the tangent line at

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

- and-values.If

, estimateusing 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.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.