Advanced Calc( Derivatives)

  • Thread starter chief12
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  • #1
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Homework Statement


function f is differential when x=0,
f'(0) is not equal to zero for all a,b(real Numbers)
f(a+b) = f(a)f(b)

show f'(x) = f'(x)f(x)


Homework Equations





The Attempt at a Solution


f(a+b) = f(a)f(b) for all a,b(real numbers)
f(0), a+b=0
then f(0) = 1

lim x-->0 f(x) = f(0) = 1

then i get stuck
 

Answers and Replies

  • #2
lanedance
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Homework Statement


function f is differential when x=0,
f'(0) is not equal to zero for all a,b(real Numbers)
f(a+b) = f(a)f(b)

show f'(x) = f'(x)f(x)

that would imply f(x) = 1 for all x... which then gives f'(x) = f'(0) = 0
also f'(0) is not equal to zero for all a,b,... does this mean only for a=-b?

are you sure this is how the question was written? try and write thinsg exactly as they are given...
 
Last edited:
  • #3
lanedance
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now guessing at what teh question actually asked... i would start by considering
f(x+0) = f(x) = f(x)f(0)
this shows f(0) = 1
 
  • #4
lanedance
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then consider f(2x)
 

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