Let f be a differentiable function on R such that f(2)=1, f^′(2)=4. Let lim_x → 0(f(2+x))^3 / x= e^α. Then the number of times the curve y=4 x^3-4…

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