The equation of the tangent to the curve $\dpi{100} y=x+\frac{4}{x^{2}},$ that is parallel to the $\dpi{100} x$-axis, is Option 1) $y=0$ Option 2) $y=1$ Option 3) $y=2$ Option 4) $y=3$

V Vakul

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.

$y = x +\frac{4}{x^{2}}$

$\frac{dy}{dx} = 1 +\frac{4.(-2)}{x^{3}}$

$0 = 1 -\frac{8}{x^{3}}$

$\therefore x^{3} = +8 \ \ \ x=+2$

$y = +2 +\frac{4}{4} = +2 +1 = 3$

Option 1)

$y=0$

This option is incorrect.

Option 2)

$y=1$

This option is incorrect.

Option 3)

$y=2$

This option is incorrect.

Option 4)

$y=3$

This option is correct.

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