In
geometry, the
tangent line (or simply
tangent) to a plane
curve at a given
point is the
straight line that "just touches" the curve at that point.
Leibniz defined it as the line through a pair of
infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where
f is the
derivative of
f. A similar definition applies to
space curves and curves in
n-dimensional
Euclidean space.