For real x, the maximum possible value of {x}/\sqrt{1+x^{4}} is

CAT 2020 Exam Shift 2 Solved Paper

Question : 60 of 76

Marks: +1, -0

For real

x

, the maximum possible value of

\;{x}/{√{1+x^{4}}}

Solution:

\;{x}/{√{1+x^{4}}}=\;{1}/{√{\;{1}/{x^{2}}+x^{2}}}

x^{2}+\;{1}/{x^{2}} ≥ 2

Hence the maximum value of

\;{1}/{√{\;{1}/{x^{2}}+x^{2}}}

\;{1}/{√{2}}

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