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Question: Answered & Verified by Expert
In the interval $(-3,3)$ the function $f(x)=\frac{x}{3}+\frac{3}{x}, x \neq 0$ is :
MathematicsApplication of DerivativesAP EAMCETAP EAMCET 2006
Options:
  • A increasing
  • B decreasing
  • C neither increasing nor decreasing
  • D partly increasing and partly decreasing
Solution:
2338 Upvotes Verified Answer
The correct answer is: decreasing
$\because \quad f(x)=\frac{x}{3}+\frac{3}{x}$
$f^{\prime}(x)=\frac{1}{3}-\frac{3}{x^2}$
It is clear that $f^{\prime}(x)$ is less than zero in the interval $(-3,3)$.
Thus $f(x)$ is decreasing in the interval $(-3,3)$.

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