The minimum value of (x^ 2 +250 x ) is: - Vidyadip

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
$=2\text{x}-\frac{250}{\text{x}^{2}}=0$
⇒ 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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