tangent line to a curve

Relate rate of change to the slope of the tangent line to a curve at a point.

The tangent line to a curve C at a point p, the osculating curve from the family of straight lines.

Graphs Tangent lines to a curve.

Connect the derivative with a particular limit, and express this limit in situations like secant and tangent lines to a curve.

The line perpendicular to the tangent line to a curve at the point of tangency is called the normal line to the curve at that point.

In this animation we see how the tangent line to a curve can be represented as the limit of a sequence of secant lines obtained by drawing a line through two points on a curve, one fixed and one variable.