- Topics At a Glance
**Derivative as a Limit of Slopes**- Slope of a Line Between Two Points
- Slope of a Line Between Two Points on a Function
- Slope at One Point?
- Estimating Derivatives Given the Formula
**Estimating Derivatives from Tables**- Finding Derivatives Using Formulas
- Derivatives as an Instantaneous Rate of Change
- Average Rate of Change
- Instantaneous Rate of Change
- Units, Words, and Notation
- Tangent Lines
- How Tangent Lines Look
- When Tangent Lines Don't Exist
- Tangent Lines and Derivatives
- Tangent Line Approximation
- Finding Tangent Lines
- Using Tangent Lines to Approximate Function Values
- Differentiability and Continuity
- The Derivative Function
- Graphs of
*f*(*x*) and*f*' (*x*) - Theorems
- Rolle's Theorem
- The Mean Value Theorem
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem
- Appendix: Speed v. Velocity

We can also estimate the derivative of a function *f* at a point *a* if we're given a table of values for *f*, but not given a formula. Check out the examples and exercises to learn how.

Example 1

Use the following table of values to estimate f'(1.2). |

Exercise 1

- Estimate
*f*'(2.5) given the following table of values:

Exercise 2

Estimate *g*'(4) given the following table of values:

Exercise 3

Estimate *f'*(*2*) given the following table of values: