Second Derivative and Concavity

If $$f''(x) > 0$$, the function is concave up, indicating that the slope of the function is increasing.

If $$f''(x) < 0$$ for all x in an interval, then the function is concave up on that interval.

The second derivative test can be used to determine intervals where a function is concave up or concave down.

A point where the second derivative changes sign is considered a point of inflection.