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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'

```
9 years ago 419 Points
```							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

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```
9 years ago
```							 f(x+y)=f(x)f(y)f(0+0)=f(0).f(0)Therefore, f(0)=1,0f`(x+y)=f'(x)f(y)+f'(y)f(x)f(0+5)=f'(0)f(5)+f'(5)f(0)  Using f(0)=0f'(5)=6
```
4 months ago
```							Dear Student,Please find below the solution to your problem.Put x=y=0 the f(0)=f2(0)f(0)=0 or 1f'(0)=lim h->0 (f(0+h)-f(0))/h= (f(0)f(h)-f(0))/h= f(0)*(f(h)-1)/hnow f(0) cant be zero as f'(0) is 3f(0)=1lim 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)/hf'(5)=f(5)*3=2*3=6 using (1)Thanks and Regards
```
4 months ago
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