Let $C^{\infty}(\mathbb{R})$ be the vector space of "smooth" functions, i.e., real-valued functions $f(x)$ in the variable $x$ that have infinitely many derivatives at all points $x \in \mathbb{R}$.

Let $D : C^{\infty}(\mathbb{R}) \to C^{\infty}(\mathbb{R})$ and $D^2 : C^{\infty}(\mathbb{R}) \to C^{\infty}(\mathbb{R})$ be the linear transformations defined by the first derivative $D(f(x)) = f'(x)$ and the second derivative $D^2(f(x)) = f''(x)$.

1. Determine whether the smooth function $g(x) = 3e^{-2x}$ is an eigenvector of $D$. If so, give the associated eigenvalue. If not, enter NONE.
   Eigenvalue =
   
   
2. Determine whether the smooth function $h(x) = \cos\!\left(3x\right)$ is an eigenvector of $D^2$. If so, give the associated eigenvalue. If not, enter NONE.
   Eigenvalue =