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# Write the Minimum Value of F(X) = X + 1 X , X > 0 . - CBSE (Science) Class 12 - Mathematics

#### Question

Write the minimum value of f(x) = $x + \frac{1}{x}, x > 0 .$

#### Solution

$\text { Given }: \hspace{0.167em} f\left( x \right) = x + \frac{1}{x}$

$\Rightarrow f'\left( x \right) = 1 - \frac{1}{x^2}$

$\text { For a local maxima or a local minima, we must have }$

$f'\left( x \right) = 0$

$\Rightarrow 1 - \frac{1}{x^2} = 0$

$\Rightarrow x^2 = 1$

$\Rightarrow x = 1, - 1$

$\text { But }x > 0$

$\Rightarrow x = 1$

$\text { Now,}$

$f''\left( x \right) = \frac{1}{x^3}$

$\text { At x} = 1:$

$f''\left( 1 \right) = \frac{2}{\left( 1 \right)^3} = 2 > 0$

$\text { So, x = 1 is a point of local minimum } .$

$\text { Thus, the local minimum value is given by }$

$f\left( 1 \right) = 1 + \frac{1}{1} = 1 + 1 = 2$

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Solution Write the Minimum Value of F(X) = X + 1 X , X > 0 . Concept: Graph of Maxima and Minima.
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