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BITSAT2012MathematicsApplication of DerivativesActual

If f ( x )= a ²-1 a ²+1 x ³-3 x +5 is a decreasing function of x in R , then the set of possible values of a (independent of x ) is

Options

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

Correct answer

C. [-1,1]

Step-by-step solution

f^ (x)=3 ( a²-1 a²+1 ) x²-3 f ^ ( x )<0 for all x if a ²-1 0 -1 a 1

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