Let \(\tilde{x}\) be a random variable with expected value \(\mathbb{E}[\tilde{x}]\) and variance \(k^{2} \sigma^{2}\), admitting the representation \(\tilde{x}=\mathbb{E}[\tilde{x}]+k \tilde{\epsilon}\), where \(\tilde{\epsilon}\) is a random variable with zero mean and variance \(\sigma^{2}\). Show that, for any strictly increasing and differentiable utility function \(u: \mathbb{R} \rightarrow \mathbb{R}\), the risk premium \(ho_{u}(\tilde{x}, k)\) parameterized by \(k\) satisfies \(ho_{u}(\tilde{x}, 0)=0\) and \(\left.\frac{\partial ho_{u}(\tilde{x}, k)}{\partial k}\right|_{k=0}=0\).