anonymous
  • anonymous
Using the First Derivative Test, find any local extema for f(x)= x^2+25/x
Calculus1
chestercat
  • chestercat
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richyw
  • richyw
well take the first derivative\[f'(x)=2x-\frac{25}{x^2}\]set this equal to zero to find extrema. \[2x=\frac{25}{x^2}\]\[2x^3=25\]\[x^3=\frac{25}{2}\]\[x=\sqrt[3]{\frac{25}{2}}\]\[x=\frac{5^{2}{3}}{\sqrt[3]{2}}\]
UnkleRhaukus
  • UnkleRhaukus
im not sure about you last line @richyw , once you have found x , substitute back into f to find f(x) and hence ( x , f(x) )
richyw
  • richyw
right, sorrt that was a typo. should be \(5^{3/2}\) if I recall correctly...

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richyw
  • richyw
I hope they caught that because I would never leave 75 written as \(5^23\) haha

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