### Home > CALC > Chapter 6 > Lesson 6.3.1 > Problem 6-87

6-87.

Consider the function ^{ }.

Find the equation of the tangent line to

^{ }at.Evaluate

to find the slope, and evaluateto find the-intercept. Use the point-slope formula to create the equation of the tangent line.Approximate

using part (a).Use the tangent line at

to evaluate. This will approximate. Why approximate?

Since a tangent is a linear equation, it is easier to evaluate than.Use

to justify whether part (b) is an under or over approximation of the actual value.A concave up graph has tangent lines that are below the curve. Sketch it, you will see.

And a concave down graph has tangent lines that are above the curve.Overestimate since