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AP EAMCET202124 Aug 2021Morning ShiftMathematicsDifferentiationActual

If 2 f(x)-3 f ( 1 x )=x+1 , then f^ ( 3 ) is equal to

Options

  1. A-1 5
  2. B3 5
  3. C- 3 5
  4. D3 5

Correct answer

A. -1 5

Step-by-step solution

aligned & 2 f(x)-3 f ( 1 x )=x+1...(i) & Replace x 1 x & 2 f ( 1 x )-3 f(x)= 1 x +1...(ii) aligned Multiply Eq. (i) by 2 and Eq. (ii) by 3 and then adding 4 f(x)-6 f ( 1 x )=2 x+2 array rlrl & & 6 f ( 1 x )-9 f(x) & = 3 x +3 & 4 f(x)-9 f(x) & =2 x+ 3 x +5 & & -5 f(x) & =2 x+ 3 x +5 & & f(x) & =- 2 5 x- 3 5 x -1 array Differentiate w.r.t. x , aligned f^ (x) & =- 2 5 + 3 5 x^2 f^ ( 3 ) & =- 2 5 + 3 5( 3 )^2 & =- 2 5 + 3 5 3 & =- 2 5 + 1 5 = -2+1 5 & =- 1 5 aligned

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