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MHT CET20228 Aug 2022Evening ShiftMathematicsApplication of DerivativesActual

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

Options

  1. A1 2
  2. B0
  3. C1 4
  4. D1 3

Correct answer

C. 1 4

Step-by-step solution

aligned & f(x)=x²⁵(1-x)⁷⁵ & f^ (x)=25 x²⁴(1-x)⁷⁵-x²⁵ 75(1-x)⁷⁴ & =25 x²⁴ (1-x)⁷⁴(1-4 x) aligned aligned & f(x) takes maximum value at x= 1 4 & aligned

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