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AP EAMCET202317 May 2023Morning ShiftMathematicsDifferential EquationsActual

If f^ (x)=a x+b x and f^ (0)=4, f(0)=3, f ( 2 )=5 , then f ( x )=

Options

  1. A2 x+4 x+1
  2. B4 x+2 x+1
  3. C2 x+3 x+1
  4. D4 x+ x+1

Correct answer

A. 2 x+4 x+1

Step-by-step solution

f^ (x)=a x+b x... (i) Given: f^ (0)=4, f(0)=3, f ( n 2 )=5 aligned & f^ (x)= (a x+b x) d x & f(x)=a x-b x+C ...(ii) & f^ (0)=a 0+b 0=a 1 4=a & f(0)=3=-b+c & f ( 2 )=5=a+c c=5-4=1 & -b+c=3 3=-b+1 b=-2 aligned In equation (ii) : f(x)=4 x+2 x+1

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