Question

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

Answer 1

well take the first derivative\[f'(x)=2x-\frac{25}{x^2}\]set this equal to zero to find extrema. \[2x=\frac{25}{x^2}\]\[2x^3=25\]\[x^3=\frac{25}{2}\]\[x=\sqrt[3]{\frac{25}{2}}\]\[x=\frac{5^{2}{3}}{\sqrt[3]{2}}\]

Answer 2

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) )

Answer 3

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

Answer 4

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