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Manipal MET2014MathematicsFunctions

If f(x+y)=f(x) f(y) for all x and y and f(15)=2, f^ (0)=3 , then f^ (5) will be

Options

  1. A2
  2. B4
  3. C6
  4. D8

Correct answer

C. 6

Step-by-step solution

Let x=5, y=0 f(5+0)=f(5) f(0) aligned f(5) & =f(5) f(0) f(0)=1 f^ (5) _ h 0 & = f(5+h)-f(5) h & = _ h 0 f(5) f(h)-f(5) h & = _ h 0 2 ( f(h)-1 h ) [ f(5)=2] & =2 _ h 0 ( f(h)-f(0) h )=2 f(0) & =2 3=6 aligned

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