1. Derivatives Using the Limit Definition
At the end of this lesson you should be able to
use the limit definition to find the derivative of a function.
find the slope of a tangent line to a given point.

2. The derivative of with respect to x is the function and is defined as,
                                                                    

3. Steps to follow Find f(x+h) Simplify f(x+h)-f(x) Put all over h
Solve the limit

4. Examples
Find the derivative of the following function using the limit definition of a derivative.

5. Now use the limit definition

6. Example 2

7. Find the slope of the tangent line to
at the point (2,3)
The derivative IS the slope of the tangent line, so to find it just plug the
x-value of the point into the derivative.
So the slope will equal 2(2)-3 = 1

8. Example 3 Find the slope of the tangent line at the point (-1,.5) for

9. Example 4 Find the derivative of the function
Use the
conjugate

10. Practice Problems

11. Answers
f’(x) = 2x-2
f’(x)=

12. Homework
Pg. 770
#6-12 even, 26,28,30,31