AP EAMCET · Maths · Application of Derivatives
The function \(f(x)=x^2+\frac{54}{x}\)
- A is increasing and has minimum value 27 in the interval \((0, \infty)\)
- B is decreasing and has neither maximum nor minimum in the interval \((-\infty, 0)\)
- C has maximum value 27 in the interval \((-\infty, \infty)\)
- D is increasing and has neither maximum nor minimum values in the interval \((-\infty, \infty)\)
Answer & Solution
Correct Answer
(B) is decreasing and has neither maximum nor minimum in the interval \((-\infty, 0)\)
Step-by-step Solution
Detailed explanation
\(f(x)=x^2+\frac{54}{x}\) \(f^{\prime}(x)=2 x-\frac{54}{x^2} < 0\) for \(x \in(-\infty, 0)\) \(\therefore f(x)\) is decrasing in \((-\infty, 0)\) and for critical points: \(f^{\prime}(x)=0 \Rightarrow 2 x-\frac{54}{x^2}=0 \Rightarrow x^3=27 \Rightarrow x=3\) So there is no…
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