anonymous
  • anonymous
what part of the graph of f'(x) determines the inflection points of f(x)???
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1440028143297:dw|
anonymous
  • anonymous
To find the inflection point you find the 2nd derivative of f(x) and then find x ( f''(x)=0 )
anonymous
  • anonymous
okay so the x intercepts of f'(x) are the inflection points on f(x) right?

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jim_thompson5910
  • jim_thompson5910
The extrema of f ' (x) have the same x coordinates of the roots of f '' (x), which is also where the inflection points on f(x) have the same x coordinates
jim_thompson5910
  • jim_thompson5910
`okay so the x intercepts of f'(x) are the inflection points on f(x) right?` incorrect
anonymous
  • anonymous
okay i think i understand , where the tangent is zero on the graph of f'(x) is where f(s) has an inflection point
jim_thompson5910
  • jim_thompson5910
sorta, it has to be an extrema
jim_thompson5910
  • jim_thompson5910
the tangent slopes have to change from positive to negative, or vice versa
anonymous
  • anonymous
what do you mean by extrema ?
jim_thompson5910
  • jim_thompson5910
let's say we had this f ' (x) graph |dw:1440028912113:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1440028941193:dw|
jim_thompson5910
  • jim_thompson5910
but it's not a local min and not a local max
jim_thompson5910
  • jim_thompson5910
we need something like this or this |dw:1440028990706:dw|
anonymous
  • anonymous
okay so where ever the graph of f'(x) has a local max or min the graph of f(x) has an inflection point ?
jim_thompson5910
  • jim_thompson5910
correct
jim_thompson5910
  • jim_thompson5910
"extrema" is a way to say "min or max" it's the extreme portion of the graph, so to speak
anonymous
  • anonymous
thank you very much i can now solve loads of problems :D
jim_thompson5910
  • jim_thompson5910
you're welcome. I'm glad it's making sense now

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