anonymous
  • anonymous
what is the critical number of 8x ln x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
what does critical number means?
lgbasallote
  • lgbasallote
it is a value of x for f'(x)=0 @suroj..as far as i know
anonymous
  • anonymous
take the derivative (using the product rule) set it equal to zero and solve for x

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anonymous
  • anonymous
d/dx lnx= 1/x knowing this, you can use the product rule 8x(1/x)+8lnx 8(1+lnx)=0 1+lnx=0 lnx=-1 e^-1=x
anonymous
  • anonymous
\[f'(x)=\frac{8x}{x}+8\ln(x)=8+8\ln(x)\] \[8(1+\ln(x))=0\] \[\ln(x)=-1\] \[x=e^{-1}\]
anonymous
  • anonymous
what dockworker said
anonymous
  • anonymous
is this even question of derivative?
anonymous
  • anonymous
what about the function x^(4/5) (x- 10) it has two critical numbers where A
anonymous
  • anonymous
i think you asked this earlier. didn't someone solve it?
anonymous
  • anonymous
critical number also occurs when the derivative is not defined if this helps you
anonymous
  • anonymous
ln(x) is not defined when x=0
anonymous
  • anonymous
i dont remember asking this earlier
anonymous
  • anonymous
maybe i did. i have a boatload of questions
anonymous
  • anonymous
\[\frac{d}{dx}x^{\frac{4}{5}}(x-10)=\frac{4}{5}x^{\frac{-1}{5}}(x-10)+x^\frac{4}{5}\] \[=\frac{4}{5x^{\frac{1}{5}}}(x-10)+x^{\frac{4}{5}}\] \[=\frac{4(x-10)+5x^{\frac{1}{5}}(x^{\frac{4}{5}})}{5x^{\frac{1}{5}}}\] \[=\frac{4x-40+5x}{5x^{\frac{1}{5}}}=\frac{9x-40}{5x^{\frac{1}{5}}}\] so the 2 critical numbers are x=40/9 and x=0, assuming i made no mistakes

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