Suppose that p(x) is some fixed distribution and that we wish to approximate it using a Gaussian distribution q(x) = N (x|μ, Σ). By writing down the form of the KL divergence KL(p q) for a Gaussian q(x) and then differentiating, show that minimization of KL(p q) with respect to μ and Σ leads to the result that μ is given by the expectation of x under p(x) and that Σ is given by the covariance.