AP Calculus AB and BC glossary

Concavity

Also called: Concave up, Concave down

Concavity describes which way a graph bends. A graph is concave up where the second derivative is positive and the slope is increasing, and concave down where the second derivative is negative and the slope is decreasing.

The clearest way to hold it is in terms of the tangent line: where a curve is concave up it lies above its tangent lines, and where it is concave down it lies below them. That fact also tells you whether a linear approximation overestimates or underestimates.

The mistake

Tying concavity to whether the function is increasing. They are independent: a function can be increasing while concave down, which is what a decelerating but still rising quantity looks like.

Appears in: Unit 5: Analytical Applications