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MHT CET202617 April 2026Morning ShiftMathematicsApplication of DerivativesActual

The function f(x) = x+3 x^2-9x+20 ,dx , then f(x) is

Options

  1. Aincreases on R
  2. Bdecreases on R - (4, 5)
  3. Cdecreases on (- , -3] (4, 5)
  4. Dincreases on (-3, )

Correct answer

C. decreases on (- , -3] (4, 5)

Step-by-step solution

Given f(x) = x+3 x^2-9x+20 ,dx Differentiating with respect to x , we get: f'(x) = x+3 x^2-9x+20 = x+3 (x-4)(x-5) For f(x) to be decreasing, f'(x) 0 . x+3 (x-4)(x-5) 0 The critical points are x = -3 , x = 4 , and x = 5 . Using the wavy curve method to determine the sign of f'(x) in different intervals: For x (5, ) , f'(x) > 0 For x (4, 5) , f'(x) For x (-3, 4) , f'(x) > 0 For x (- , -3) , f'(x) Therefore, f'(x) 0 for x (- , -3] (4, 5) . Hence, f(x) decreases on (- , -3] (4, 5) . Answer: decreases on (- , -3] (4, 5)

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