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