Let \(f\) be a differentiable function on \(R\) such that \(f(2)=1\), \({f}^{'}(2)=4\). Let \(\lim _{x \rightarrow 0}(f(…

Let \(f\) be a differentiable function on \(R\) such that \(f(2)=1\), \({f}^{'}(2)=4\). Let \(\lim _{x \rightarrow 0}(f(2+x))^{\frac{3}{x}}=e^{\alpha}\). Then the number of times the curve \(y=4{x}^{3}-4{x}^{2}-4(\alpha -7)x-\alpha\) meets x -axis is :-

[JEE Main 2025, 4 Apr (Shift 2)]