### Home > CALC > Chapter 6 > Lesson 6.2.2 > Problem6-77

6-77.

Find y' and use point slope form to find the equation.

Point slope form: y = m(xx1) + y1

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

The base and height are given on the graph.

Compute y'(1) and use point slope form again to find the equation.

$\text{For a point }\left (a, \frac{1}{a} \right ),\text{use the result of } y'(a) \text{ and point slope form to find the equation of the tangent line.}$

The vertices of the triangle made by the tangent line are (0, 0), (0, t(0)), and (x-intercept of t(x), 0), where t(x) is the equation of the tangent line.

Calculate the area of the triangle using the vertices to determine the dimensions.