AP Calculus AB and BC glossary
Corner
A corner is a point where a graph changes direction abruptly, with left and right derivatives that are different finite numbers. The function is continuous there but not differentiable, because no single tangent slope exists.
The absolute value function has a corner at the origin: the slope is approaching from the left and from the right. Both one-sided derivatives exist and are finite, which is exactly what distinguishes a corner from a cusp.
Corners are common at the seams of piecewise functions and anywhere an absolute value appears, so check those points before claiming a function is differentiable everywhere.
Appears in: Unit 2: Defining the Derivative