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MHT CET202012 Oct 2020Evening ShiftMathematicsIndefinite IntegrationActual

If f^ (x)=k( x+ x) and f(0)=9, f ( 2 )=15 , then f(x)=

Options

  1. A3( x- x)+12
  2. B3( x- x)-12
  3. C3( x+ x)+12
  4. D3( x+ x)-12

Correct answer

A. 3( x- x)+12

Step-by-step solution

f^ (x)=k( x+ x) On integrating both sides, we get f(x)=k( x- x)+Cf(0)=k(0-1)+Cf(0)=-k+C -k+C=9 ...(1) Also f ( 2 )=k ( 2 - 2 )+C15=k+C ...(2) Adding (1) &(2) we get 2 C=24 C=12 k=3 f(x)=3( x- x)+12

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