Let $$\begin{gathered}
p ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 2 x , x \in \mathbb { R } \\
f _ { 0 } ( x ) = \begin{cases} \int _ { 0 } ^ { x } p ( t ) d t , & x \geq 0 \\ - \int _ { x } ^ { 0 } p ( t ) d t , & x < 0 \end{cases} \\
f _ { 1 } ( x ) = e ^ { f _ { 0 } ( x ) } , \quad f _ { 2 } ( x ) = e ^ { f _ { 1 } ( x ) } , \quad \ldots \quad , f _ { n } ( x ) = e ^ { f _ { n - 1 } ( x ) }
\end{gathered}$$ How many roots does the equation $\frac { d f _ { n } ( x ) } { d x } = 0$ have in the interval $( - \infty , \infty ) ?$ (A) 1 . (B) 3 . (C) $n + 3$. (D) $3n$.
Let
$$\begin{gathered}
p ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 2 x , x \in \mathbb { R } \\
f _ { 0 } ( x ) = \begin{cases} \int _ { 0 } ^ { x } p ( t ) d t , & x \geq 0 \\ - \int _ { x } ^ { 0 } p ( t ) d t , & x < 0 \end{cases} \\
f _ { 1 } ( x ) = e ^ { f _ { 0 } ( x ) } , \quad f _ { 2 } ( x ) = e ^ { f _ { 1 } ( x ) } , \quad \ldots \quad , f _ { n } ( x ) = e ^ { f _ { n - 1 } ( x ) }
\end{gathered}$$
How many roots does the equation $\frac { d f _ { n } ( x ) } { d x } = 0$ have in the interval $( - \infty , \infty ) ?$\\
(A) 1 .\\
(B) 3 .\\
(C) $n + 3$.\\
(D) $3n$.