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AP EAMCET202125 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

Find the absolute maximum of x⁴⁰-x²⁰ on the interval [0,1] .

Options

  1. A-1 4
  2. B0
  3. C1 4
  4. D1 2

Correct answer

B. 0

Step-by-step solution

Let aligned f(x) & =x⁴⁰-x²⁰ f^ (x) & =40 x³⁹-20 x¹⁹ f^ (x) & =0 20 x¹⁹ (2 x²⁰-1 )=0 x & =0, x=1 f(0) & =0 f(1) & =0 aligned Maximum value of x⁴⁰-x²⁰ in [0,1] is 0 .

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