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

  • Understand the derivative as a function related to the original definition of a function.
  • Find the derivative function using the limit definition.
  • Relate the derivative function to the derivative at a point.
  • Explain the relationship between differentiability and continuity.
  • Relate the graph of the function to the graph of its derivative.
  • Determine whether a piecewise function is differentiable.