In geometry, a line that intersects a circle exactly once; in calculus, a line that touches a curve at one point and whose slope is equal to that of the curve at that point.
Particularly useful as approximations of curves in the immediate vicinity of the point of tangency, tangent lines are the basis of many estimation techniques, including linear approximation . The numerical value of the slope of the tangent line to the graph of a function at any point equals that of the function's derivative at that point. This is one of the keystones of differential calculus . See also differential geometry .