Discussion Forum

If f is differentiable  , $f(x+y)=f(x)f(y)$ for all  $x,y\in IR$, f(3)=3, f'(0)=11, then f'(3)=

Answer:

Explanation:

 We have,

  f(x+y)=f(x)f(y)

 differentiate with respect to x, y as constant , we get

  $f'(x+y)=f'(x) f(y)$

 Put x=0 , y=3 we get

 f'(0+3)=f'(0).f(3)

$\Rightarrow$     f'(3) =f'(0).f(3)

$\Rightarrow$  f'(3)=11 x3 =33    $[\because f'(0)=11, f(3)=3]$