Q34 / 90 · JEE Main 2010 · Mathematics

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

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

Solution

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

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

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