Let C[infinity](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∈R. Let D:C[infinity](R)→C[infinity](R) and D2:C[infinity](R)→C[infinity](R) be the linear transformations defined by the first derivative D(f(x))=f′(x) and the second derivative D2(f(x))=f′′(x) a. Determine whether the smooth function g(x)=7e−2x is an eigenvector of D. If so, give the associated eigenvalue. If not, enter NONE. Eigenvalue = b. Determine whether the smooth function h(x)=sin(8x) is an eigenvector of D2. If so, give the associated eigenvalue. If not, enter NONE. Eigenvalue =