1. Maxima and Minima of Functions
Maxima and minima of functions occur where there is a change from increasing to decreasing, or vice versa.

2. Maxima and Minima of Functions
Maxima and minima of functions occur where there is a change from increasing to decreasing, or vice versa. -3 4

3. Maxima and Minima of Functions
Maxima and minima of functions occur where there is a change from increasing to decreasing, or vice versa.
Relative Max. -3 4

4. Maxima and Minima of Functions
Maxima and minima of functions occur where there is a change from increasing to decreasing, or vice versa.
Relative Max.
Relative Min. -3 4

5. Maxima and Minima of Functions

6. Maxima and Minima of Functions

7. Maxima and Minima of Functions

8. Maxima and Minima of Functions

9. Maxima and Minima of Functions

10. Maxima and Minima of Functions

11. Maxima and Minima of Functions

12. Maxima and Minima of Functions
DECREASING
INCREASING

13. Maxima and Minima of Functions

14. Maxima and Minima of Functions
Relative Minimum

15. Maxima and Minima of Functions

16. Maxima and Minima of Functions

17. Maxima and Minima of Functions

18. Maxima and Minima of Functions

19. Maxima and Minima of Functions

20. Maxima and Minima of Functions

21. Maxima and Minima of Functions

22. Maxima and Minima of Functions
INCREASING
DECREASING
INCREASING

23. Maxima and Minima of Functions
Relative Maximum
Relative Minimum

24. Maxima and Minima of Functions

25. Maxima and Minima of Functions
The difference in this example is we are restricted to a specific interval. So the edges of the interval will act as critical points along with the ones we find using the first derivative. They will be relative max or min depending on their position.

26. Maxima and Minima of Functions
The difference in this example is we are restricted to a specific interval. So the edges of the interval will act as critical points along with the ones we find using the first derivative. They will be relative max or min depending on their position.
Moving left to right :
If the edge has a decreasing arrow following, it is a relative maximum.
If the edge has an increasing arrow following, it is a relative minimum.
If the edge has a decreasing arrow in front of it, it is a relative minimum.
If the edge has an increasing arrow in front of it, it is a relative maximum.

27. Maxima and Minima of Functions
Moving left to right :
If the edge has a decreasing arrow following, it is a relative maximum.
If the edge has an increasing arrow following, it is a relative minimum.
If the edge has a decreasing arrow in front of it, it is a relative minimum.
If the edge has an increasing arrow in front of it, it is a relative maximum.

28. Maxima and Minima of Functions
Moving left to right :
If the edge has a decreasing arrow following, it is a relative maximum.
If the edge has an increasing arrow following, it is a relative minimum.
If the edge has a decreasing arrow in front of it, it is a relative minimum.
If the edge has an increasing arrow in front of it, it is a relative maximum.

29. Maxima and Minima of Functions
Moving left to right :
If the edge has a decreasing arrow following, it is a relative maximum.
If the edge has an increasing arrow following, it is a relative minimum.
If the edge has a decreasing arrow in front of it, it is a relative minimum.
If the edge has an increasing arrow in front of it, it is a relative maximum.

30. Maxima and Minima of Functions
Moving left to right :
If the edge has a decreasing arrow following, it is a relative maximum.
If the edge has an increasing arrow following, it is a relative minimum.
If the edge has a decreasing arrow in front of it, it is a relative minimum.
If the edge has an increasing arrow in front of it, it is a relative maximum.

31. Maxima and Minima of Functions
Moving left to right :
If the edge has a decreasing arrow following, it is a relative maximum.
If the edge has an increasing arrow following, it is a relative minimum.
If the edge has a decreasing arrow in front of it, it is a relative minimum.
If the edge has an increasing arrow in front of it, it is a relative maximum.

32. Maxima and Minima of Functions
Moving left to right :
If the edge has a decreasing arrow following, it is a relative maximum.
If the edge has an increasing arrow following, it is a relative minimum.
If the edge has a decreasing arrow in front of it, it is a relative minimum.
If the edge has an increasing arrow in front of it, it is a relative maximum.

33. Maxima and Minima of Functions
Moving left to right :
If the edge has a decreasing arrow following, it is a relative maximum.
If the edge has an increasing arrow following, it is a relative minimum.
If the edge has a decreasing arrow in front of it, it is a relative minimum.
If the edge has an increasing arrow in front of it, it is a relative maximum.

34. Maxima and Minima of Functions
Relative Maximum
Moving left to right :
If the edge has a decreasing arrow following, it is a relative maximum.
If the edge has an increasing arrow following, it is a relative minimum.
If the edge has a decreasing arrow in front of it, it is a relative minimum.
If the edge has an increasing arrow in front of it, it is a relative maximum.

35. Maxima and Minima of Functions
Relative Maximum
This is neither because there is no change in increasing/decreasing. It is called an “inflection point” which we will discuss later…
Moving left to right :
If the edge has a decreasing arrow following, it is a relative maximum.
If the edge has an increasing arrow following, it is a relative minimum.
If the edge has a decreasing arrow in front of it, it is a relative minimum.
If the edge has an increasing arrow in front of it, it is a relative maximum.

36. Maxima and Minima of Functions
Relative Maximum
Relative Minimum
Change from decreasing to increasing…
Moving left to right :
If the edge has a decreasing arrow following, it is a relative maximum.
If the edge has an increasing arrow following, it is a relative minimum.
If the edge has a decreasing arrow in front of it, it is a relative minimum.
If the edge has an increasing arrow in front of it, it is a relative maximum.

37. Maxima and Minima of Functions
Relative Maximum
Relative Minimum
Relative Maximum
Moving left to right :
If the edge has a decreasing arrow following, it is a relative maximum.
If the edge has an increasing arrow following, it is a relative minimum.
If the edge has a decreasing arrow in front of it, it is a relative minimum.
If the edge has an increasing arrow in front of it, it is a relative maximum.