In mathematics, a tangent line is a straight line that touches a curve
or a function at a single point without crossing it. At the point of
contact, the tangent line has the same slope as the curve, representing
the instantaneous rate of change of the function at that specific
location. Tangent lines are used to approximate the behavior of a
function near a particular point and are fundamental in calculus for
understanding local properties of functions and finding critical points.