Question

Determine the extreme values of f(x) = x + 1/ sqrt (x) . 1 < x < 9

Answer 1

start with the derivative, get \(1-\frac{1}{2\sqrt{x^3}}\) set equal to zero and solve

Answer 2

\[2\sqrt{x^3}-1=0\]
\[\sqrt{x^3}=\frac{1}{2}\]
\[x^3=\frac{1}{4}\]
\[x=\frac{1}{\sqrt[3]{4}}\]

Answer 3

check the critical point and the end point
biggest is biggest, smallest is smallest