anonymous
  • anonymous
the value of c for which f(x)=x+(c/x) has a local minimum at x=3 is?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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zepdrix
  • zepdrix
If x=3 is a local minimum point, then x=3 corresponds to a critical point, ya?\[\large\rm f'(3)=0\]
zepdrix
  • zepdrix
Take derivative, set equal to 0, (since we're looking for critical points) Plug in x=3, (since that corresponds to a critical point) solve for c.
anonymous
  • anonymous
so x+c/x is 1+c(x^-1) right then c-x^-2=0?

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zepdrix
  • zepdrix
woah not sure what happened there, looks like you took derivative of the first term twice or something.
zepdrix
  • zepdrix
and yes, the negative comes down, but make sure you're not wring c MINUS x^-2, that's multiplication
zepdrix
  • zepdrix
\[\large\rm x+cx^{-1}\qquad\to\qquad 1+-cx^{-2}\]
zepdrix
  • zepdrix
writing* not wring lol
anonymous
  • anonymous
oh okay. 1-cx^-2=0 -1/-(3^-2)=9 Thanks!
zepdrix
  • zepdrix
9? Good good good :)

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