Equation of tangent to the curve y=x+4/(x^2) which is parallel to X -axis is

Correct answer: (C) y=3. y=x+4/(x^2) ⇒ y^′=1-8/(x^3) As tangent is parallel to X -axis, y^′=0 ⇒ x=2 At x=2, y=3 . ∴ Equation of tangent is y=3

Q105 / 160 · AP EAMCET 2022 (07 Jul Shift 2) · Mathematics

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

A
$y=8$
B
$y=0$
Correct answer
C
$y=3$
D
$y=2$

Solution

$$ y=x+\frac{4}{x^2} \Rightarrow y^{\prime}=1-\frac{8}{x^3} $$ As tangent is parallel to $X$-axis, $y^{\prime}=0 \Rightarrow x=2$ At $x=2, y=3$. $\therefore$ Equation of tangent is $y=3$

Hence, the correct answer is option: 'C'.

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