anonymous
  • anonymous
y= (x^2-9)/(x^2+1) find the max, min points and the inflection points
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
i first used the qoutient rule: which i got x^2(2x)(1-9)/9x^2-1)^2 WHATS NEXT?
anonymous
  • anonymous
simplified, my derivative came out to (20x)/(x^2+1)^2
anonymous
  • anonymous
ok but do i now equal that to 0 to find the min and max points?

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anonymous
  • anonymous
for second derivative i got -20(3x^2-1)/(x^2+1)^3
anonymous
  • anonymous
set the first derivative to zero to find critical numbers.
anonymous
  • anonymous
so it should look like 20x/(x^2+1)^3=0
anonymous
  • anonymous
lemme double check...
anonymous
  • anonymous
yep... http://www.wolframalpha.com/input/?i=derivative+of+%28x%5E2-9%29%2F%28x%5E2%2B1%29
anonymous
  • anonymous
do you want me to go over how that first derivative is obtained?
anonymous
  • anonymous
can u tell how to solve for the first max point?
Zarkon
  • Zarkon
paunic88: you want 20x/(x^2+1)^2=0 see dpaInc's derivative from above
anonymous
  • anonymous
ok so the max value is 1/3?
anonymous
  • anonymous
and the min is -1/3
Zarkon
  • Zarkon
no
anonymous
  • anonymous
set the derivative's numerator to zero which will give you 20x = 0 so x = 0. this is the x coodinate where your max/min will occur.
anonymous
  • anonymous
notice also that this function is defined for all real numbers so you don't have to worry about discontinuities
anonymous
  • anonymous
still there?

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