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Question

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


A
y=1
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B
y=2
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C
y=3
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D
y=0
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Solution

The correct option is C $$\mathrm{y}=3$$
 $$\displaystyle {y}={x}+\frac{4}{x^{2}}$$ 

$$\Rightarrow \displaystyle \frac{dy}{dx}=1-\frac{8}{x^{3}}$$

Since, tangent is parallel to x-axis i.e. $$ \displaystyle \frac{dy}{dx}=0$$

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

$$x^3=8$$

$$\Rightarrow x=2$$

substitute in the equation of the curve

$$y=2+\dfrac{4}{2^2}=2+\dfrac{4}{4}=2+1$$

$$\Rightarrow y=3$$        
.
Equation of tangent is given as 

$${y}-3=0({x}-2) $$   [slope-point form]

$$\Rightarrow y-3=0$$ 

Hence, option 'C' is correct.

Mathematics

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