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

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

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