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To find the inflection point you find the 2nd derivative of f(x) and then find x ( f''(x)=0 )
okay so the x intercepts of f'(x) are the inflection points on f(x) right?
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
`okay so the x intercepts of f'(x) are the inflection points on f(x) right?` incorrect
okay i think i understand , where the tangent is zero on the graph of f'(x) is where f(s) has an inflection point
sorta, it has to be an extrema
the tangent slopes have to change from positive to negative, or vice versa
what do you mean by extrema ?
let's say we had this f ' (x) graph |dw:1440028912113:dw|
but it's not a local min and not a local max
we need something like this or this |dw:1440028990706:dw|
okay so where ever the graph of f'(x) has a local max or min the graph of f(x) has an inflection point ?
"extrema" is a way to say "min or max" it's the extreme portion of the graph, so to speak
thank you very much i can now solve loads of problems :D
you're welcome. I'm glad it's making sense now