A Shapes-of-Graphs Game

Misc

Problem set on linear approximation, extreme values, Mean Value Theorem. See handout for details.

Questions?

The Shapes of Graphs

Section 4.5 in the textbook.

Graphing Game

Goal: see how closely someone else can reproduce a graph you have in mind using only information about the signs of its derivatives and limited information about its value.

Play:

1. Team 1 comes up with a shape they can describe as the graphs of one or more continuous functions over certain domains.
2. Team 1 gives team 2 information about the values of their functions at the left and right ends of their domains, and the signs (positive, negative, or zero) of their function(s) derivatives over intervals in the domains.
3. Team 2 draws their best estimate of team 1’s function(s).

Play this for a while….

Another Aspect of Shape

How do graphs “end,” i.e., what happens as x gets very large or very small?

Often there is some identifiable pattern to the behavior, i.e., the function heads to positive or negative infinity, it levels off, etc.

Next

Limits at infinity.

Read section 4.6.