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  4. The equation of the tangent to the curve y = x +(4/x2), that is parallel to the x-axis, is

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Q. The equation of the tangent to the curve $y = x +\frac{4}{x^{2}}, $ that is parallel to the $x-axis$, is

AIEEEAIEEE 2010Application of Derivatives

Solution:

Parallel to x-axis $\quad\Rightarrow \frac{dy}{dx} = 0\quad\Rightarrow 1-\frac{8}{x^{3}} = 0$
$\Rightarrow x = 2\quad\Rightarrow y = 3$
Equation of tangent is $y - 3 = 0\left(x - 2\right)\quad\Rightarrow y - 3 = 0 $