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AP EAMCET202022 Sep 2020Morning ShiftMathematicsDifferentiationActual

If f(x)= | array ccc x & x & 1 2 x & x^2 & 2 x x & x & 1 array | , then the value of f^ (x) at x=0 is equal to

Options

  1. A-1
  2. B1
  3. C2
  4. D0

Correct answer

D. 0

Step-by-step solution

aligned & Given, f(x)= | array ccc x & x & 1 2 x & x^2 & 2 x x & x & 1 array | & f^ (x)= | array ccc - x & 1 & 0 2 x & x^2 & 2 x x & x & 1 array |+ | array ccc x & x & 1 2 x & 2 x & 2 x & x & 1 array | & + | array ccc x & x & 1 2 x & x^2 & 2 x ^2 x & 1 & 0 array | & aligned So, at x=0, f^ (x)= | array ccc 0 & 1 & 0 0 & 0 & 0 0 & 0 & 1 array |+ | array lll 1 & 0 & 1 2 & 0 & 2 0 & 0 & 1 array | + | array lll 1 & 0 & 1 0 & 0 & 0 1 & 1 & 0 array |=0

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