1. Sec 2.8: THE DERIVATIVE AS A FUNCTION replace a by x

2. Sec 2.8: THE DERIVATIVE AS A FUNCTION Slopes : 0 + -

3. Sec 2.8: THE DERIVATIVE AS A FUNCTION

8. Definition: A function f is differentiable on an open interval (a, b) if it is differentiable at every number in the interval. Definition: A function f is differentiable on an open interval (a, b) if it is differentiable at every number in the interval.

9. Sec 2.8: THE DERIVATIVE AS A FUNCTION 2 properties continuity differentiability Proof: Remark: f cont. at af diff. at a Remark: f discont. at af not diff. at a Remark: f discont. at a f not diff. at a

10. Sec 2.8: THE DERIVATIVE AS A FUNCTION Example: f cont. at af diff. at a f discont. at af not diff. at a f discont. at a f not diff. at a

11. Sec 2.8: THE DERIVATIVE AS A FUNCTION Example: f cont. at af diff. at a f discont. at af not diff. at a f discont. at a f not diff. at a

12. Sec 2.8: THE DERIVATIVE AS A FUNCTION HOW CAN A FUNCTION FAIL TO BE DIFFERENTIABLE?

13. Sec 2.8: THE DERIVATIVE AS A FUNCTION Higher Derivative Note: jerk acceleration velocity

15. MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag R

16. R H

18. H

19. H H

20. H R R

21. H H H R