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.
Ohio Transfer Module Mathematics, Statistics, and Logic (TMM) Standards
Core TMM005 Outcome: Core skill demonstrated by students who successfully complete a Calculus I Course
Standard: Determine the derivative of a function using the limit definition and derivative theorems. Interpret the derivative as the slope of a tangent line to a graph, the slope of a graph at a point, and the rate of change of a dependent variable with respect to an independent variable.