Question

Let $f\left(\frac{x+y}{2}\right)=\frac{f\left(x\right)+f\left(y\right)}{2}$ and $f^1\left(0\right)$ and $f\left(0\right)=b$ then $f^1\left(x\right)$ is equal to

• A. 0
• B. a
• C. b
• D. a+b

Answer 1

The correct option is A

0

As per green relation , f is a linear polynomial
$\therefore f\left(x\right)=Ax+B$
$\therefore f^{11}\left(x\right)=0$