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MHT CET202611 April 2026Morning ShiftMathematicsApplication of DerivativesActual

The difference between the local extreme values of the function f(x) = 2x^3 - 15x^2 + 36x + 40 is ......

Options

  1. A4
  2. B3
  3. C2
  4. D1

Correct answer

D. 1

Step-by-step solution

Given f(x) = 2x^3 - 15x^2 + 36x + 40 Differentiating with respect to x : f'(x) = 6x^2 - 30x + 36 For local extrema, f'(x) = 0 : 6(x^2 - 5x + 6) = 0 (x - 2)(x - 3) = 0 x = 2, 3 Evaluating the function at the critical points: f(2) = 2(2)^3 - 15(2)^2 + 36(2) + 40 = 16 - 60 + 72 + 40 = 68 f(3) = 2(3)^3 - 15(3)^2 + 36(3) + 40 = 54 - 135 + 108 + 40 = 67 The difference between the local extreme values is 68 - 67 = 1 . Answer: 1

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