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Maxima-Minima type of questions in Algebra generally tend to give students jitters as they struggle to find the correct way about the question without wasting too much time. What is the best way to practice questions of this kind and keep on track with your online CAT preparation? One of the best ways to achieve this is to practice CAT previous year paper by yourself and prepare yourself to attempt such questions in full swing if they appear in your upcoming CAT Question Paper. Instead of fearing questions of this type, practice dilligently so that you can conquer them in your CAT exam.

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}{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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