### Home > APCALC > Chapter 6 > Lesson 6.2.2 > Problem 6-77

The graph of

Write the equation of the tangent line.

Find

and use point slope form to find the equation.Point slope form:

Explain why the tangent line will always give an under approximation of the curve using the second derivative.

If the graph was concave down, would the tangent line be an over or under-approximation?

Calculate the area of the shaded triangle.

The base and height are given on the graph.

Calculate the area of the triangle formed when the tangent is instead placed at

. Compute

and use point slope form again to find the equation.Prove that the area of the shaded triangle formed by a tangent to

is always the same, regardless of the point of tangency. The vertices of the triangle made by the tangent line are

, , and ( -intercept of, whereis the equation of the tangent line.Calculate the area of the triangle using the vertices to determine the dimensions.