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MHT CET202620 April 2026Morning ShiftMathematicsApplication of DerivativesActual

On the interval [0, 1] , the function f(x) = x²⁵(1 - x)⁷⁵ attains its maximum value at the point x = ....

Options

  1. A0
  2. B1 4
  3. C1 2
  4. D1 3

Correct answer

B. 1 4

Step-by-step solution

Given f(x) = x²⁵(1 - x)⁷⁵ Differentiating with respect to x : f'(x) = 25x²⁴(1 - x)⁷⁵ - 75x²⁵(1 - x)⁷⁴ f'(x) = 25x²⁴(1 - x)⁷⁴ [ (1 - x) - 3x ] f'(x) = 25x²⁴(1 - x)⁷⁴ (1 - 4x) For maximum or minimum, f'(x) = 0 25x²⁴(1 - x)⁷⁴ (1 - 4x) = 0 x = 0, 1, 1 4 At x = 0 and x = 1 , f(x) = 0 . For x (0, 1) , f(x) > 0 . Thus, f(x) attains its maximum value at x = 1 4 . Answer: 1 4

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