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MHT CET202525 Apr 2025Morning ShiftMathematicsApplication of DerivativesActual

f (x)= x 2 + 2 x , x 0 is stricity decreasing in

Options

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

Correct answer

C. (-2,2)

Step-by-step solution

To determine where the function f(x) = x 2 + 2 x is strictly decreasing , we analyze its derivative, f'(x) = 1 2 - 2 x^2 , and solve f'(x) 1 2 - 2 x^2 Considering the domain x 0 , f(x) is strictly decreasing on (-2, 0) and (0, 2) . Option C, (-2, 2) , represents the union of these intervals, excluding the discontinuity at x = 0 , and is the correct choice.

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