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Rapid environmental changes are putting numerous species at risk of extinction. For migration-limited species, persistence depends on either phenotypic plasticity or evolutionary adaptation (evolutionary rescue). Current theory on evolutionary rescue typically assumes linear environmental change. Yet accelerating environmental change may pose a bigger threat. Here, we present a model of a species encountering an environment with accelerating or decelerating change, to which it can adapt through evolution or phenotypic plasticity (within-generational or transgenerational). We show that unless either form of plasticity is sufficiently strong or adaptive genetic variation is sufficiently plentiful, accelerating or decelerating environmental change increases extinction risk compared to linear environmental change for the same mean rate of environmental change.