### Home > APCALC > Chapter 6 > Lesson 6.3.1 > Problem 6-90

6-90.

Consider the function .

Write the equation of the line tangent 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 your answer to 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.Is your approximation an underestimate or an overestimate of the actual value? Explain.

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