Determining Concavity

What is happening to the tangent lines in a graph as you go from left to right?

concave up - they are increasing
concave down - they are decreasing

The second derivative is a rate of change of the first derivative.

if f''(x) > 0, then concave up.
if f''(x) < 0, then concave down.

Use Mr. Smiley and Mr. Frowny to help you remember this:

Send any comments or questions to: David Pleacher