Tangent and Secant lines

Definition

  • A tangent line is a line which touches a curve at only one point
  • A secant line is a line which touches a curve at 2 points

As Q approaches P, the slope of the secant is a very good estimate of the slope of the tangent.

Formulas

  1. with 2 points, and
  2. with 2 points and

Example

Find the equation of the tangent, in standard form, to the curve at

Find the value of in terms of

Find the value of

Using formula 1, find the slope of the tangent line

See Limit Laws

With , get the equation of the line using the slope formula