PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# If(X) = X+ 1 X ,X > 0, Then Its Greatest Value is (A) − 2 (B) 0 (C) 3 (D) None of These - PUC Karnataka Science Class 12 - Mathematics

#### Question

If(x) = x+$\frac{1}{x}$,x > 0, then its greatest value is _______________ .

• -2

• 0

• 3

• none of these

#### Solution

none of these

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

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

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

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

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

$\Rightarrow x^2 - 1 = 0$

$\Rightarrow x^2 = 1$

$\Rightarrow x = \pm 1$

$\Rightarrow x = 1 ................\left( \text { Given }: x>0 \right)$

$\text { Now,}$

$f''\left( x \right) = \frac{2}{x^3}$

$\Rightarrow f''\left( 1 \right) = 2 > 0$

$\text { So, x = 1 is a local minima } .$

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Solution If(X) = X+ 1 X ,X > 0, Then Its Greatest Value is (A) − 2 (B) 0 (C) 3 (D) None of These Concept: Graph of Maxima and Minima.
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