- 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
Introduction to :
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.
Practice:
Example 1
Use the following table of values to estimate f'(1.2).
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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:
