To improve performance and meet power constraints, vendors are introducing heterogeneous multicores that combine high performance and low power cores. However, choosing which cores and scheduling applications on them remain open problems. This paper presents a scheduling algorithm that provably minimizes energy on heterogeneous multicores and meets latency constraints for interactive applications, such as search, recommendations, advertisements, and games. Because interactive applications must respond quickly to satisfy users, they impose multiple constraints, including average, tail, and maximum latency. We introduce SEM (Slow-to-fast, Energy optimization for Multiple constraints), which minimizes energy by choosing core speeds and how long to execute jobs on each core. We prove SEM minimizes energy without a priori knowledge of job service demand, satisfies multiple latency constraints simultaneously, and only migrates jobs from slower to faster cores. We address practical concerns of migration overhead and congestion. We prove optimizing energy for average latency requires homogeneous cores, whereas optimizing energy for tail and deadline constraints requires heterogeneous cores. For interactive applications, we create a formal foundation for scheduling and selecting cores in heterogeneous systems.