Question

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

• A. $y=0$
• B. $y=1$
• C. $y=2$
• D. $y=3$

Answer 1

The correct option is D

$y=3$

Find the equation of the tangent of the given curve

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

We know that, slope of the line parallel to $x$-axis $=0$.

So, the slope of required tangent is $=0$

That means $\frac{dy}{dx}=0$

$$\begin{gathered} \Rightarrow \frac{d}{dx}\left(x+\frac{4}{x^2}\right)=0 \\ \Rightarrow 1–\frac{8}{x^3}=0 \\ \Rightarrow x^3=8 \\ \Rightarrow x=2 \end{gathered}$$

By substituting the value of $x$ in the given equation of curve we get,

$$\begin{gathered} y=2+\frac{4}{2^2} \\ \Rightarrow y=2+\frac{4}{4} \\ \Rightarrow y=3 \end{gathered}$$

Hence, the correct answer is option $\left(D\right)$.