Question

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

• A. $y=8$
• B. $y=0$
• C. $y=3$
• D. $y=2$

Answer 1

The correct option is C $y=3$

$\frac{dy}{dx}=0$
$\Rightarrow 1-\frac{8}{x^3}=0$
$\Rightarrow x=2$
$y=2+\frac{4}{2^2}$
$\Rightarrow y=3$
Equation of Tangent at $(2,3)$ is

$y-3=0(x-2)\Rightarrow y=3$