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AP EAMCET202421 May 2024Morning ShiftMathematicsApplication of DerivativesActual

The number of all the values of x for which the function f(x)= x+ 1- ^2 x 1+ ^2 x attains its maximum value on [0,2 ] is

Options

  1. A4
  2. B1
  3. C2
  4. Dinfinite

Correct answer

C. 2

Step-by-step solution

aligned & f(x)= x+ 1- ^2 x 1+ ^2 x f(x)= x+ 2 x & f^ (x)= x-2 2 x=0 x=2 2 x & 1=2 x x= 6 x=n +(-1)^n 6 aligned Only two values are possible in [0,2 ] which are 6 , 5 6

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