We consider the problem of finding N-point configurations on a d-dimensional Euclidean sphere with the smallest absolute maximum value of their total potential over the sphere. The kernel is the value of a given potential function f at the Euclidean distance squared, where f is continuous on [0,4] and completely monotone on (0,4] modulo an additive constant. We show that any sharp configuration, which is antipodal or is a spherical design of an even strength is a solution to this problem. We also prove that the absolute maximum over the sphere of the potential of any such configuration is attained at points of that configuration.