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Question 10 : For real x, the maximum possible value of \\frac{x}{√(1 + x^{4})}) is

  1. 1
  2. \\frac{1}{2})
  3. \\frac{1}{√2})
  4. \\frac{1}{√3})

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Explanatory Answer

Dividing by x on both numerator and denominator
\\frac{1}{\sqrt{\frac{1+x^{4}}{x^{2}}}})=\\frac{1}{\sqrt{\frac{1}{x^{2}}+x^{2}}})
\\frac{1}{x^{2}}) + x2 ≥ 2
√[\\frac{1}{x^{2}})+x2] ≥ √2
\\frac{1}{\sqrt{\frac{1}{x^{2}}+x^{2}}}) ≤ \\frac{1}{\sqrt{2}})


The question is "For real x, the maximum possible value of \\frac{x}{√(1 + x^{4})}) is"

Hence, the answer is, "\\frac{1}{√2})"

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