anonymous
  • anonymous
critical point of f(x) -3/x^2+9
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Derivative set equal to zero and solve.
anonymous
  • anonymous
The derivative is\[-3 (x ^{2}+9)(2x)\]
anonymous
  • anonymous
x^2+9 is the denominator?

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anonymous
  • anonymous
Yes, to the -2, forgot to add that.
anonymous
  • anonymous
yes
anonymous
  • anonymous
use the quotient rule
anonymous
  • anonymous
6x/(x^2+9x)2??
anonymous
  • anonymous
i mean 6x/(x^2+9x)^2?
anonymous
  • anonymous
\[f'(x)=\frac{-3(2x)}{(x^2+9)^2}=\frac{-6x}{(x^2+9)^2}\]
anonymous
  • anonymous
@Dockworker has it
anonymous
  • anonymous
actually, numerator is positive
anonymous
  • anonymous
\[f"(x)=\frac{6x}{(x^2+9)^2}\]
anonymous
  • anonymous
Yes, forgot the negative in front of the 3
anonymous
  • anonymous
f'(x), not f''(x) rather :)
anonymous
  • anonymous
set that equal to zero?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
yes, normally for critical numbers you'd find the zeros and when the derivative is undefined, but because the denominator can never be 0 in this case, there's only one critical number
anonymous
  • anonymous
is it 0?
anonymous
  • anonymous
If you plug it into Wolfram Alpha you can check your answer.
anonymous
  • anonymous
they gave me 0
anonymous
  • anonymous
thank you

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