MCQ
The minimum value of $(\text{x}^{2}+\frac{250}{\text{x}})$ is:
  • $75$
  • B
    $50$
  • C
    $25$
  • D
    $55$

Answer

Correct option: A.
$75$
$\text{f}(\text{x})=\text{x}^{2}+\frac{250}{\text{x}}$
$\text{f}'(\text{x})=2\text{x}-\frac{250}{\text{x}^{2}}$
For the local minima a or maxima. We must have $f'(x) = 0$
$=2\text{x}-\frac{250}{\text{x}^{2}}=0$
$\Rightarrow x = 5$
$=2\text{x}-\frac{250}{\text{x}^{2}}=0$
$\text{f}''(\text{x})=2+\frac{500}{\text{x}^{3}}$
$\text{f}''(\text{x})=2+\frac{500}{125}>0$
function has minima at $x = 5$
$f(5) = 75.$

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