Definition of the derivative modules
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 of a function at a given point.
- Recognize and distinguish between secant and tangent lines.
- Recognize the the tangent line as a local approximation for a differentiable function near a point.
Slope of a curve
Two young mathematicians discuss the novel idea of the ``slope of a curve.''
The definition of the derivative
We compute the instantaneous growth rate by computing the limit of average growth rates.