If $f\left(x\right)$ is a differentiable function such that $f^{\prime }\left(x\right)=7-\frac{3}{4}\frac{f\left(x\right)}{x}$, \displaystyle{f}

If $f\left(x\right)$ is a differentiable function such that $f^{\prime }\left(x\right)=7÷||/||\frac{f\left(x\right)}{x}$, $f\left(1\right)\ne 4$, then $\underset{x\to 0^{+}}{\lim }x\cdot f\left(\frac{1}{x}\right)$ is equal to (a) does not exist (b) exist and equal to 4 (c) exist and is equal to $\frac{4}{7}$ (d) exists and equal to 0