Q108 / 160 · AP EAMCET 2006 · Mathematics

In the interval $(-3,3)$ the function $f(x)=\frac{x}{3}+\frac{3}{x}, x \neq 0$ is :

  • A
    increasing
  • Correct answer
    B
    decreasing
  • C
    neither increasing nor decreasing
  • D
    partly increasing and partly decreasing

Solution

$\because \quad f(x)=\frac{x}{3}+\frac{3}{x}$ $f^{\prime}(x)=\frac{1}{3}-\frac{3}{x^2}$ It is clear that $f^{\prime}(x)$ is less than zero in the interval $(-3,3)$. Thus $f(x)$ is decreasing in the interval $(-3,3)$.

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

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