## maddypeoples 3 years ago Using the First Derivative Test, find any local extema for f(x)= x^2+25/x

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1. 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}}$

2. 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) )

3. richyw

right, sorrt that was a typo. should be $$5^{3/2}$$ if I recall correctly...

4. richyw

I hope they caught that because I would never leave 75 written as $$5^23$$ haha