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NDA2026MathematicsApplication of DerivativesActual

Passage: Let S and T be the sets where f(x)= x^3 3 - 5x^2 2 +6x+7 decreases and increases respectively. Question: What is T equal to ?

Options

  1. Ax 2 x 3
  2. Bx 3
  3. C(2,3)
  4. D[2,3]

Correct answer

A. x 2 x 3

Step-by-step solution

Given f(x) = x^3 3 - 5x^2 2 + 6x + 7 Differentiating with respect to x , we get: f'(x) = x^2 - 5x + 6 f'(x) = (x - 2)(x - 3) For the function to be increasing, f'(x) 0 (x - 2)(x - 3) 0 This inequality holds true for x 2 or x 3 . Therefore, the set T where the function increases is x 2 x 3 . Answer: x 2 x 3

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