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AP EAMCET202421 May 2024Morning ShiftMathematicsApplication of DerivativesActual

If f(x)=x^ x , then the interval in which f(x) decreases is

Options

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

Correct answer

A. [0, 1 e ]

Step-by-step solution

aligned & f(x)=x^x y=x^x & y=x x & 1 y d y d x = x+1 d y d x =x^x(1+ x) aligned Since, x^x is always +ve f(x) decreases when 1+ 0 x 1 x 1 e f(x) decreases when x [0, 1 e ]

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