Achieving real-time agility and adaptation with respect to changing requirements in existing IT infrastructure can pose a complex challenge. We describe a goal-oriented approach to manage this complexity. We argue that a goal-oriented perspective can form an effective basis for devising and deploying responses to changed requirements at runtime. We offer an extended vocabulary of goal types by presenting two novel conceptions: differential goals and integral goals, which we formalize in both linear-time and branching-time settings. We describe goal lifecycles and interactions and the extended notion of context for the representation of rapidly changing, complex operating environments. We then illustrate the working of the approach by presenting a detailed scenario of adaptation in a Kubernetes setting, in the face of a Distributed Denial-of-Service (DDoS) attack.