marcelie
  • marcelie
can someone please tell me whats the difference between absolute min / max and local min/ max?
Mathematics
chestercat
  • chestercat
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IrishBoy123
  • IrishBoy123
|dw:1442652853333:dw|
IrishBoy123
  • IrishBoy123
|dw:1442653632424:dw|
IrishBoy123
  • IrishBoy123
chart courtesy of : http://tutorial.math.lamar.edu/Classes/CalcI/MinMaxValues.aspx

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marcelie
  • marcelie
\[f(x) = x^4 +x \]
marcelie
  • marcelie
is there a local min ?
IrishBoy123
  • IrishBoy123
suspect you have plotted it and got f'(x)=0 etc, etc so what do you think?
marcelie
  • marcelie
i think there is a loacl min bc it is the lowest
marcelie
  • marcelie
i graphed this and this is how my graph is
marcelie
  • marcelie
|dw:1442700904192:dw|
IrishBoy123
  • IrishBoy123
|dw:1442700981127:dw|
marcelie
  • marcelie
i would think its local min ? bc its the lowest ..
IrishBoy123
  • IrishBoy123
"local"
marcelie
  • marcelie
|dw:1442701109539:dw|
IrishBoy123
  • IrishBoy123
|dw:1442701182855:dw|
marcelie
  • marcelie
i would say theres no abs max bc we cant calculate how far its going up . so theres no abs max .
marcelie
  • marcelie
i would say local min
IrishBoy123
  • IrishBoy123
so it gets smaller somewhere else?
IrishBoy123
  • IrishBoy123
as in more negative
IrishBoy123
  • IrishBoy123
abs max = \(\infty\) look at the right and left ends of the curve, what does f(x) do?!
marcelie
  • marcelie
its getting bigger ?
marcelie
  • marcelie
bc there no end bc keeps going on and on ?
IrishBoy123
  • IrishBoy123
|dw:1442701371065:dw|
marcelie
  • marcelie
ohhh... so then itll be abs min bc its the lowest ?
marcelie
  • marcelie
so itlll mostly be local min / max when it makes a curve ?
marcelie
  • marcelie
|dw:1442701539914:dw|
IrishBoy123
  • IrishBoy123
yes abs max = \(\infty\) abs min = whatever that bottom point is, because it never gets smaller
marcelie
  • 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 ?
IrishBoy123
  • IrishBoy123
i think it is easy to over-complicate this :p draw some curves and let's take it from there
marcelie
  • marcelie
|dw:1442701817981:dw|
marcelie
  • marcelie
|dw:1442701867282:dw|
marcelie
  • marcelie
|dw:1442701894696:dw|
marcelie
  • marcelie
then abs min would be same as local min ?
IrishBoy123
  • IrishBoy123
|dw:1442701971501:dw|
marcelie
  • marcelie
wait... there would of been abs min but keeps goin on but nope theres no.
IrishBoy123
  • IrishBoy123
abs max and min are \(\infty\) and \(-\infty\) local max and min are whatever they are.
marcelie
  • marcelie
ah okay.
IrishBoy123
  • IrishBoy123
|dw:1442702187388:dw|
marcelie
  • marcelie
abs max /min is the y vlaue ? locla min/max is the x and y values ?
IrishBoy123
  • IrishBoy123
in all cases you are concerned with the value of y because we are looking at 2D
IrishBoy123
  • IrishBoy123
so the global maximum is a question of how big and/or small y becomes as \(\infty \lt x \lt \infty\)
marcelie
  • marcelie
okay. is there an easier way to find abs max/min and local max/min ?
IrishBoy123
  • IrishBoy123
it depends on the curve but mostly calculus is king. eg find the max/min of \(y = 2x^{51} + 3x^{425} - 2\)
IrishBoy123
  • IrishBoy123
|dw:1442704184202:dw|
IrishBoy123
  • IrishBoy123
|dw:1442704379317:dw|
marcelie
  • marcelie
|dw:1442726412311:dw|

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