Derivatives as functions modules
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.
Wait for the right moment
Two young mathematicians discuss derivatives as functions.
The derivative as a function
Here we study the derivative of a function, as a function, in its own right.
Differentiability implies continuity
We see that if a function is differentiable at a point, then it must be continuous at that point.