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

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

A

75

B

50

C

25

D

55

Text Solution

Verified by Experts

The correct Answer is:
A
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`.
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