After completing this section, students should be able to do the following.

  • Use limits to find the slope of the tangent line at a point.
  • Understand the definition of the derivative at a point.
  • Compute the derivative of a function at a point.
  • Estimate the slope of the tangent line graphically.
  • Write the equation of the tangent line to a graph at a given point.
  • Recognize and distinguish between secant and tangent lines.
  • Recognize different notation for the derivative.
  • Recognize the the tangent line as a local approximation for a differentiable function.