AP EAMCET · Maths · Application of Derivatives
In the interval \((-3,3)\) the function \(f(x)=\frac{x}{3}+\frac{3}{x}, x \neq 0\) is :
- A increasing
- B decreasing
- C neither increasing nor decreasing
- D partly increasing and partly decreasing
Answer & Solution
Correct Answer
(B) decreasing
Step-by-step Solution
Detailed explanation
\(\because \quad f(x)=\frac{x}{3}+\frac{3}{x}\) \(f^{\prime}(x)=\frac{1}{3}-\frac{3}{x^2}\) 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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