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KCET2013MathematicsApplication of Derivatives

The function f(x)= x 3 + 3 x decreases in the interval

Options

  1. A(-3,3)
  2. B(- , 3)
  3. C(3, )
  4. D(-9,9)

Correct answer

A. (-3,3)

Step-by-step solution

Given, f(x)= x 3 + 3 x On differentiating w.r.t. x , we get f^ (x)= 1 3 - 3 x² Since, function is decreasing array ll i.e., & f^ (x) < 0 & 1 3 - 3 x² < 0 & 1 3 < 3 x² & x² < 9 & x (-3,3) array which is the required interval in which function f(x) decreases.

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