abstract: The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. Much of the theoretical focus on linear response has been on establishing that for various classes of systems, there is a principle of linear response. Our focus in this work is in a much less studied direction, namely, determining those perturbations that lead to 'maximal' response. The practical implication of optimizing response is that it allows the identification of the perturbations that provoke a maximal system response. Under a suitable setting, we consider selecting the perturbations that (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the expectation of the linear response with respect to an observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. Furthermore, application of the theory to various dynamics will be given.