challenge: According to the center manifold existence theorem, what is required for the right-hand side function f(x) to guarantee the existence of a center manifold at every equilibrium point?
  
  A. It must be a polynomial function of degree r
  B. It must be continuously differentiable only once
  C. It must be a linear function of x
  D. It must be C^r (r times continuously differentiable)
  Answer: 