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BITSAT2012MathematicsDifferentiationActual

Let f(x+y)=f(x) f(y) for all x, y where f(0) 0 If f(5)=2 and f^ (0)=3, then f^ (5) is equal to-

Options

  1. A6
  2. B0
  3. C1
  4. DNone of these

Correct answer

A. 6

Step-by-step solution

f^ (5)= _ h 0 f(5+h)-f(5) h = _ h 0 f(5+h)-f(5+0) h = _ h 0 f(5) f(h)-f(5)+f(0) h ( f(x+y)=f(x), f(y) for all x, y)= ( _ h 0 f(h)-f(0) h ) f(5)=f^ (0) f(5)=3 2=6

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