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AP EAMCET201824 Apr 2018Morning ShiftMathematicsContinuity and DifferentiabilityActual

If f: R R is a differentiable function such that f(x+y)=f(x) . f(y) for all x, y R and if f^ (4)=24 and f^ (0)=3 , then f(4)=

Options

  1. A72
  2. B5
  3. C11
  4. D8

Correct answer

D. 8

Step-by-step solution

aligned & Let x=4, y=0 f(4+0)=f(4) f(0) & aligned f(4) & =f(4) f(0) f(0)=1 f^ (4) & = _ h 0 f(4+h)-f(4) h & = _ h 0 f(4) f(h)-f(4) h = _ h 0 ( f(h)-1 h ) f(4) aligned aligned aligned & f^ (4)=f(4) _ h 0 (f(h)-f(0) h & f^ (4)=f(4) f^ (0) & f^ (4)=24, f^ (0)=3 f(4)= f^ (4) f^ (0) = 24 3 =8 . aligned

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