The minimum value of `(x^2+(250)/(x))` is

Options

A. 75
B. 50
C. 25
D. 55

Answer

A

Explanation

Let `y=f(x)=(x^(2)+(250)/(x)),because(dy)/(dx)=f^(`)(x)=2x-(250)/(x^(2))`
Put `f^(`)(x)=0implies2x^(3)-250=0impliesx^(3)=125impliesx=5`
Again, `(d^(2)y)/(dx^(2))=f^(``)(x)=2+(500)/(x^(3))`. Now `f^(``)(5)=2+(500)/(125)gt0`
Hence at `x=5`. The function will be minimum.
Minimum value `f^(5)=25+50=75`.