When the function y = f (x) is concave up, the graph of its derivative y = f '(x) is increasing. When the function y = f (x) is concave down, the graph of its derivative y = f '(x) is decreasing.

How do you know when concavity changes?

To find when a function is concave, you must first take the 2nd derivative, then set it equal to 0, and then find between which zero values the function is negative. Now test values on all sides of these to find when the function is negative, and therefore decreasing.

What does it mean when the concavity changes?

If the concavity of f changes at a point (c,f(c)), then f′ is changing from increasing to decreasing (or, decreasing to increasing) at x=c. That means that the sign of f″ is changing from positive to negative (or, negative to positive) at x=c.