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BITSAT 2012
Exam
BITSAT
Year
2012
Subject
Mathematics
Chapter
Application of Derivatives

BITSAT 2012 · Mathematics · Application of Derivatives

If f(x)= ^ 2 -1 ^ 2 +1 ^ 3 -3 x+5 is a decreasing function of x in...

If f(x)=\mathrma2−1\mathrma2+1\mathrmx3−3x+5\mathrm{f}(\mathrm{x})=\frac{\mathrma^{2}-1}{\mathrma^{2}+1} \mathrmx^{3}-3 \mathrm{x}+5 is a decreasing function of x\mathrm{x} in R\mathbf{R}, then the set of possible values of a (independent of x\mathrm{x} ) is

Options

  1. A(1,∞)(1, \infty)
  2. B(−∞,−1)(-\infty,-1)
  3. C[-1,1]
  4. DNone of these

Correct answer

C. [-1,1]

Step-by-step solution

f′(x)=3(a2−1a2+1)x2−3\mathrmf′(x)<0f^{\prime}(x)=3\left(\frac{a^{2}-1}{a^{2}+1}\right) x^{2}-3\mathrmf^{\prime}(\mathrm{x})< 0 for all x\mathrm{x} if \mathrma2−1≤0⇒−1≤a≤1\mathrma^{2}-1 \leq 0 \Rightarrow-1 \leq \mathrm{a} \leq 1
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