AP EAMCET · Maths · Application of Derivatives
In the interval \(\left(\frac{1}{\mathrm{e}}, \mathrm{e}\right)\), a decreasing function among the following functions is
- A \(f(x)=\frac{\log x}{x}\)
- B \(f(x)=x^2 \log x\)
- C \(f(x)=x \log x\)
- D \(f(x)=x^{-x}\)
Answer & Solution
Correct Answer
(D) \(f(x)=x^{-x}\)
Step-by-step Solution
Detailed explanation
The best way to approach this question is, find \(1^{\text {st }}\) derivative of all the function at \(x \in\left(\frac{1}{e}, e\right)\) you can choose \(x=\frac{2}{e}, \frac{3}{e} \in\left(\frac{1}{e}, e\right) \cdot\) If \(f^{\prime}(x)\) is -ve at any point in the given…
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