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COMEDK20269 May 2026Evening ShiftMathematicsApplication of DerivativesActual

If f(x) = x^3 + 3 2 x^2 + 3x + 3 , then f(x) is

Options

  1. AOdd function
  2. BEven function
  3. CIncreasing function
  4. DDecreasing function

Correct answer

C. Increasing function

Step-by-step solution

Given function is f(x) = x^3 + 3 2 x^2 + 3x + 3 . Differentiating with respect to x , we get: f'(x) = 3x^2 + 3x + 3 f'(x) = 3(x^2 + x + 1) The discriminant of the quadratic x^2 + x + 1 is D = 1^2 - 4(1)(1) = -3 Since the leading coefficient is positive and D 0 for all x R . Therefore, f'(x) > 0 for all x R . This implies that f(x) is an increasing function. Answer: Increasing function

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