### Home > CALC > Chapter 6 > Lesson 6.3.1 > Problem6-86

6-86.

Sketch the graph of $y = 2^x$ and its inverse. Label all intercepts.

1. Find the equation of the line tangent to the graph of $y = 2^x$ at its $y$-intercept.

Use point-slope form.

2. Find the equation of the line tangent to the graph of $y =\operatorname{log}_2 x$ at its $x$-intercept.

Refer to hint in part (a).

3. Graph both of these lines. What is their relationship?

Sketch the tangent lines. Are they parallel? Are they perpendicular? Neither?
Look at their equations... describe a pattern you see in their slopes.

4. Use the tangent line in part (a) to approximate the value of $y$ when $x = 0.1$. Is your estimate an under or over approximation of the actual value? How do you know using concavity?

Recall that the concavity of the graph determines whether tangent lines lie above or below the curve.