Forum Question: Choices

We all make choices. With those choices come consequences, some good and some not so good. As we learn and grow, we become more mindful of the consequences of our choices.

Today is Virtual Wednesday. You have the choice of joining our face-to-face class, or attending a virtual classroom of your own. The topic is the Derivative of the Inverse of a Function. You will find the objective of the lesson in Exploration 4.5A posted under Student Handouts on our CRMS Calculus website. After working through this Exploration, answer the following seven questions in your Forum Post:

1. State the Derivative of the Inverse of a Function property in words.

2. Using the Equation Editor (right sidebar), state this property in symbols.

3. The volume of a sphere is a function of its radius:

Is volume an invertible function?

4. Use the Equation Editor (right sidebar) to write the inverse function for the radius of a sphere as a function of its volume, r(V).

5. Using the online graphing tool (right sidebar) or another graphing tool, plot the following four graphs:
(1) The volume function, V(r);
(2) Choose any point on V(r) and graph the tangent line through this point.
(3) The inverse function r(V);
(4) Graph the tangent line through the “mirror” point on the graph of the inverse function.
* Note: The graphing window should clearly display all four graphs.

6. Show that the slopes of these tangents are reciprocals.

7. Briefly explain your choice of either coming to class or attending your virtual classroom.