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marcelie

  • one year ago

can someone please tell me whats the difference between absolute min / max and local min/ max?

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  1. IrishBoy123
    • one year ago
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    |dw:1442652853333:dw|

  2. IrishBoy123
    • one year ago
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    |dw:1442653632424:dw|

  3. IrishBoy123
    • one year ago
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    chart courtesy of : http://tutorial.math.lamar.edu/Classes/CalcI/MinMaxValues.aspx

  4. marcelie
    • one year ago
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    \[f(x) = x^4 +x \]

  5. marcelie
    • one year ago
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    is there a local min ?

  6. IrishBoy123
    • one year ago
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    suspect you have plotted it and got f'(x)=0 etc, etc so what do you think?

  7. marcelie
    • one year ago
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    i think there is a loacl min bc it is the lowest

  8. marcelie
    • one year ago
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    i graphed this and this is how my graph is

  9. marcelie
    • one year ago
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    |dw:1442700904192:dw|

  10. IrishBoy123
    • one year ago
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    |dw:1442700981127:dw|

  11. marcelie
    • one year ago
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    i would think its local min ? bc its the lowest ..

  12. IrishBoy123
    • one year ago
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    "local"

  13. marcelie
    • one year ago
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    |dw:1442701109539:dw|

  14. IrishBoy123
    • one year ago
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    |dw:1442701182855:dw|

  15. marcelie
    • one year ago
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    i would say theres no abs max bc we cant calculate how far its going up . so theres no abs max .

  16. marcelie
    • one year ago
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    i would say local min

  17. IrishBoy123
    • one year ago
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    so it gets smaller somewhere else?

  18. IrishBoy123
    • one year ago
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    as in more negative

  19. IrishBoy123
    • one year ago
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    abs max = \(\infty\) look at the right and left ends of the curve, what does f(x) do?!

  20. marcelie
    • one year ago
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    its getting bigger ?

  21. marcelie
    • one year ago
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    bc there no end bc keeps going on and on ?

  22. IrishBoy123
    • one year ago
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    |dw:1442701371065:dw|

  23. marcelie
    • one year ago
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    ohhh... so then itll be abs min bc its the lowest ?

  24. marcelie
    • one year ago
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    so itlll mostly be local min / max when it makes a curve ?

  25. marcelie
    • one year ago
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    |dw:1442701539914:dw|

  26. IrishBoy123
    • one year ago
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    yes abs max = \(\infty\) abs min = whatever that bottom point is, because it never gets smaller

  27. marcelie
    • one year ago
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    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
    • one year ago
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    i think it is easy to over-complicate this :p draw some curves and let's take it from there

  29. marcelie
    • one year ago
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    |dw:1442701817981:dw|

  30. marcelie
    • one year ago
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    |dw:1442701867282:dw|

  31. marcelie
    • one year ago
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    |dw:1442701894696:dw|

  32. marcelie
    • one year ago
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    then abs min would be same as local min ?

  33. IrishBoy123
    • one year ago
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    |dw:1442701971501:dw|

  34. marcelie
    • one year ago
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    wait... there would of been abs min but keeps goin on but nope theres no.

  35. IrishBoy123
    • one year ago
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    abs max and min are \(\infty\) and \(-\infty\) local max and min are whatever they are.

  36. marcelie
    • one year ago
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    ah okay.

  37. IrishBoy123
    • one year ago
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    |dw:1442702187388:dw|

  38. marcelie
    • one year ago
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    abs max /min is the y vlaue ? locla min/max is the x and y values ?

  39. IrishBoy123
    • one year ago
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    in all cases you are concerned with the value of y because we are looking at 2D

  40. IrishBoy123
    • one year ago
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    so the global maximum is a question of how big and/or small y becomes as \(\infty \lt x \lt \infty\)

  41. marcelie
    • one year ago
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    okay. is there an easier way to find abs max/min and local max/min ?

  42. IrishBoy123
    • one year ago
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    it depends on the curve but mostly calculus is king. eg find the max/min of \(y = 2x^{51} + 3x^{425} - 2\)

  43. IrishBoy123
    • one year ago
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    |dw:1442704184202:dw|

  44. IrishBoy123
    • one year ago
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    |dw:1442704379317:dw|

  45. marcelie
    • one year ago
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    |dw:1442726412311:dw|

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