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

Consider the curve

*xe*^{5}= 3^{y}*y.*Homework Help ✎Find

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

If

*x*= 0.1, estimate*y*using the tangent line.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.