1. DERIVATIVE OF A FUNCTION 1.5

2. DEFINITION OF A DERIVATIVE OTHER FORMS: OPERATOR:,,,

3. DERIVATIVES ****THE DERIVATIVE IS A FUNCTION. IF YOU PLUG IN AN X VALUE, THE DERIVATIVE WILL TELL YOU THE SLOPE OF THE TANGENT LINE AT THAT X VALUE.

4. EXAMPLE 1 A)FIND THE DERIVATIVE: B)FIND THE SLOPE OF THE TANGENT LINE AT X=2

5. EXAMPLE 2 FIND DY/DX:

6. EXAMPLE

7. DIFFERENTIABILITY A FUNCTION IS DIFFERENTIABLE EVERYWHERE THAT THE DERIVATIVE EXISTS.

8. WHAT IT LOOKS LIKE TO NOT BE DIFFERENTIABLE AT A CORNER AT A CUSP AT A VERTICAL TANGENT AT A DISCONTINUITY

9. ONE SIDED DERIVATIVES SHOW THAT THE FOLLOWING FUNCTION IS NOT DIFFERENTIABLE AT X = 0

10. APPROXIMATE THE VALUE OF THE DERIVATIVE F(X) F’(1) F’(3) F’(2) F’(-1)

11. SKETCHING THE GRAPH GIVEN F(X) GRAPH F’(X)

12. HOMEWORK PG 144 #25, 26 ANSWER THE QUESTION AND APPROXIMATE THE VALUE OF F’(X1), F’(X7) PG 156 #1-31 ODD