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KVPY2016MathematicsApplication of Derivatives

The range of the polynomial p(x)=4 x³-3 x as x varies over the interval (- 1 2 , 1 2 ) is

Options

  1. A[-1,1]
  2. B(-1,1]
  3. C(-1,1)
  4. D(- 1 2 , 1 2 )

Correct answer

C. (-1,1)

Step-by-step solution

P ^ ( x )=12 x ²-3=3 (4 x ²-1 ) In (- 1 2 , 1 2 ) P ^ ( x ) < 0 P ( x ) is decreasing Range ( P (-1), P (1)) Range (-1,1)

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