The apex of a curve is its highest point. Geometric use of the term "apex" generally refers to solids or to shapes with corners such as triangles. In autoracing and other motor sports, the apex is the point on the track that is closest to the inside of a curve.
An apex is a special type of vertex. A vertex is generally a corner of a figure, a common endpoint for two or more sides. In the case of curves, which do not have corners, a vertex is the sharpest point of the curve. Usually, this is some maximum or minimum value along the vertical axis. An apex is the highest vertex. In motorsports, the apex of a curve is a key concept for finding the best point on a track to start a turn in order to get the best racing time.