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f(x+y)=f(x).f(y)andf(5)=2 f'(0)=3 then f'(5)=? for all value of'x'and'y'

f(x+y)=f(x).f(y)andf(5)=2 f'(0)=3 then f'(5)=? for all value of'x'and'y'

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3 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
12 years ago

Dear Praveen

Put x=y=0 the f(0)=f2(0)

f(0)=0 or 1

f'(0)=lim h->0 (f(0+h)-f(0))/h= (f(0)f(h)-f(0))/h= f(0)*(f(h)-1)/h

now f(0) cant be zero as f'(0) is 3

f(0)=1

lim h->0 (f(h)-1)/h = f'(0)=3  .............(1)

f'(5)=lim h->0 (f(5+h)-f(5))/h= (f(5)f(h)-f(5))/h= f(5)*(f(h)-1)/h

f'(5)=f(5)*3=2*3=6     using (1)

 

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IIT Delhi

 

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Dimple Ravi Naik
15 Points
2 years ago
 
f(x+y)=f(x)f(y)
f(0+0)=f(0).f(0)
Therefore, f(0)=1,0
f`(x+y)=f'(x)f(y)+f'(y)f(x)
f(0+5)=f'(0)f(5)+f'(5)f(0)
 
 
Using f(0)=0
f'(5)=6
Rishi Sharma
askIITians Faculty 646 Points
2 years ago
Dear Student,
Please find below the solution to your problem.

Put x=y=0 the f(0)=f2(0)
f(0)=0 or 1
f'(0)=lim h->0 (f(0+h)-f(0))/h= (f(0)f(h)-f(0))/h= f(0)*(f(h)-1)/h
now f(0) cant be zero as f'(0) is 3
f(0)=1
lim h->0 (f(h)-1)/h = f'(0)=3 .............(1)
f'(5)=lim h->0 (f(5+h)-f(5))/h= (f(5)f(h)-f(5))/h= f(5)*(f(h)-1)/h
f'(5)=f(5)*3=2*3=6 using (1)

Thanks and Regards

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