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