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JEE Main20246 Apr 2024Morning ShiftMathematicsApplication of DerivativesActual

The interval in which the function f(x)=x^x, x>0 , is strictly increasing is

Options

  1. A(0, 1 e ]
  2. B(0, )
  3. C. [ 1 e , ) ]_V
  4. D[ 1 e^2 , 1 )

Correct answer

C. . [ 1 e , ) ]_V

Step-by-step solution

aligned & f ( x )= x ^ x ; x >0 & nn = x n x & 1 y dy dx = x x + n & dy dx = x ^ x (1+ n x) aligned for strictly increasing aligned & d y d x 0 x^x(1+ n x) 0 & n x -1 aligned aligned & x e⁻¹ & x 1 e & x [ 1 e , ) aligned

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