MHT CET · Maths · Application of Derivatives
If \(2 \mathrm{f}(x)+3 \mathrm{f}\left(\frac{1}{x}\right)=x^2+1, x \neq 0\) and \(\mathrm{y}=5 x^2 \mathrm{f}(x)\), then y is strictly increasing in
- A \(\left(0, \frac{1}{2}\right)\)
- B \(\left(\frac{-2}{5}, 0\right)\)
- C \(\left(\frac{1}{2}, \frac{\sqrt{5}}{2}\right)\)
- D \(\left(\frac{-1}{2}, 0\right)\)
Answer & Solution
Correct Answer
(A) \(\left(0, \frac{1}{2}\right)\)
Step-by-step Solution
Detailed explanation
\(2 \mathrm{f}(x)+3 \mathrm{f}\left(\frac{1}{x}\right)=x^2+1\) \(3 \mathrm{f}(x)+2 \mathrm{f}\left(\frac{1}{x}\right)=\frac{1}{x^2}+1\)
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