# The real number $\dpi{100} x$ when added to its inverse gives the minimum value of the sum at $\dpi{100} x$ equal to Option 1) 1 Option 2) -1 Option 3) -2 Option 4) 2

As we learnt in

Rate Measurement -

Rate of any of variable with respect to time is rate of measurement. Means according to small change in time how much other factors change is rate measurement:

$\Rightarrow \frac{dx}{dt},\:\frac{dy}{dt},\:\frac{dR}{dt},(linear),\:\frac{da}{dt}$

$\Rightarrow \frac{dS}{dt},\:\frac{dA}{dt}(Area)$

$\Rightarrow \frac{dV}{dt}(Volume)$

$\Rightarrow \frac{dV}{V}\times 100(percentage\:change\:in\:volume)$

- wherein

Where dR / dt  means Rate of change of radius.

$x + \frac{1}{x} = y$

$1 - \frac{1}{x^{2}} = \frac{\mathrm{dy} }{\mathrm{d} x} = 0$

$x^{2} = 1$

$x = 1$

Option 1)

1

This option is correct.

Option 2)

-1

This option is incorrect.

Option 3)

-2

This option is incorrect.

Option 4)

2

This option is incorrect.

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