If $y=x^3-a{x}^2+48x+7$ is an increasing function for all real values of x, then a lies in

$$\begin{gathered} y=x^3-a{x}^2+48x+7 \\ \frac{dy}{dx}=3x^2-2ax+48 \\ for increa\sin g function \frac{dy}{dx}>0 \\ \Rightarrow 3x^2-2ax+48>0 \\ \Rightarrow D<0 \\ \Rightarrow 4a^2-4\left(144\right)>0 \\ \Rightarrow a^2-144>0 \end{gathered}$$
$\Rightarrow$ $a\in (-12,12)$