### Home > CALC > Chapter Ch7 > Lesson 7.1.3 > Problem 7-31

7-31.

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.