Question

If $f(x+y)=f\left(x\right)f\left(y\right),f\left(3\right)=3,f^{\prime }\left(0\right)=11$. Then $f^{\prime }\left(3\right)$ is equal to.

• A. $11.e^{33}$
• B. $33$
• C. $11$
• D. $g\left(33\right)$

Answer 1

The correct option is B $33$

$f(x+y)=f\left(x\right)f\left(y\right)$

so, differentiate with $x$

$f^{\prime }(x+y)=f\left(y\right)f^{\prime }\left(x\right)$

Put $x=0$

so, $f^{\prime }\left(y\right)=f\left(y\right)f^{\prime }\left(0\right)$

$f^{\prime }\left(0\right)=11$

so, $f^{\prime }\left(y\right)=11f\left(y\right)$

now $f^{\prime }\left(y\right)=11f\left(y\right)$

$f^{\prime }\left(3\right)=11f\left(3\right)$

$f^{\prime }\left(3\right)=33$