Question

Let $f$ be a differentiable function satisfying $f(x+2y)=2yf\left(x\right)+xf\left(y\right)-3xy+1\forall x,yϵR$ such that $f^{\prime }\left(0\right)=1$ then $f\left(2\right)$ is

• A. 4
• B. 1
• C. 5
• D. 3

Answer 1

The correct option is D 3

$\text{If}x=0,y=0\Rightarrow f\left(0\right)=1$
$\text{If}y=0,\text{then}f\left(x\right)=xf\left(0\right)+1$
$\Rightarrow f\left(x\right)=x+1\therefore f\left(2\right)=3$