## marcelie one year ago can someone please tell me whats the difference between absolute min / max and local min/ max?

1. IrishBoy123

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2. IrishBoy123

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3. IrishBoy123

chart courtesy of : http://tutorial.math.lamar.edu/Classes/CalcI/MinMaxValues.aspx

4. marcelie

$f(x) = x^4 +x$

5. marcelie

is there a local min ?

6. IrishBoy123

suspect you have plotted it and got f'(x)=0 etc, etc so what do you think?

7. marcelie

i think there is a loacl min bc it is the lowest

8. marcelie

i graphed this and this is how my graph is

9. marcelie

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10. IrishBoy123

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11. marcelie

i would think its local min ? bc its the lowest ..

12. IrishBoy123

"local"

13. marcelie

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14. IrishBoy123

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15. marcelie

i would say theres no abs max bc we cant calculate how far its going up . so theres no abs max .

16. marcelie

i would say local min

17. IrishBoy123

so it gets smaller somewhere else?

18. IrishBoy123

as in more negative

19. IrishBoy123

abs max = $$\infty$$ look at the right and left ends of the curve, what does f(x) do?!

20. marcelie

its getting bigger ?

21. marcelie

bc there no end bc keeps going on and on ?

22. IrishBoy123

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23. marcelie

ohhh... so then itll be abs min bc its the lowest ?

24. marcelie

so itlll mostly be local min / max when it makes a curve ?

25. marcelie

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26. IrishBoy123

yes abs max = $$\infty$$ abs min = whatever that bottom point is, because it never gets smaller

27. marcelie

oh okay . lets say if i have 2 abs max ? so that means theres no abs max bc it exist 2. so it could only be one abs max ?

28. IrishBoy123

i think it is easy to over-complicate this :p draw some curves and let's take it from there

29. marcelie

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30. marcelie

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31. marcelie

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32. marcelie

then abs min would be same as local min ?

33. IrishBoy123

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34. marcelie

wait... there would of been abs min but keeps goin on but nope theres no.

35. IrishBoy123

abs max and min are $$\infty$$ and $$-\infty$$ local max and min are whatever they are.

36. marcelie

ah okay.

37. IrishBoy123

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38. marcelie

abs max /min is the y vlaue ? locla min/max is the x and y values ?

39. IrishBoy123

in all cases you are concerned with the value of y because we are looking at 2D

40. IrishBoy123

so the global maximum is a question of how big and/or small y becomes as $$\infty \lt x \lt \infty$$

41. marcelie

okay. is there an easier way to find abs max/min and local max/min ?

42. IrishBoy123

it depends on the curve but mostly calculus is king. eg find the max/min of $$y = 2x^{51} + 3x^{425} - 2$$

43. IrishBoy123

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44. IrishBoy123

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45. marcelie

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