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COMEDK2015MathematicsDifferentiation

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

Options

  1. A5
  2. B6
  3. C0
  4. DNone of these

Correct answer

B. 6

Step-by-step solution

We have, f(x+y)=f(x) f(y) Putting x=y=0 array ll & f(0+0)=f(0) f(0) & f(0)=[f(0)]² & f(0)=1 Now, f^ (5)= _ h 0 f(5+h)-f(5) h = & _ h 0 f(5) f(h)-f(5) = _ h 0 f(5) [ f(h)-1 h ] = & f(5) _ h 0 [ f(h)-f(0) h ] f(0)=1 = & 2 f^ (0)=2 3=6 array

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