Tangent Line

Definition

A tangent line is a straight line that touches a curve at only one point without crossing through it. In calculus, we use tangent lines to approximate curves and find instantaneous rates of change.

Related terms

Secant Line: A secant line intersects a curve at two points, helping us estimate average rates of change between those points.

Derivative: The derivative gives us the slope (rate of change) of a function at any given point on its graph. It helps us find tangent lines and analyze functions' behavior.

Concavity: Concavity describes whether a curve bends upward (concave up) or downward (concave down). We determine concavity by analyzing the second derivative of a function.