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Although wearable accelerometers can successfully recognize activities and detect falls, their adoption in real life is low because users do not want to wear additional devices. A possible solution is an accelerometer inside a wrist device/smartwatch. However, wrist placement might perform poorly in terms of accuracy due to frequent random movements of the hand. In this paper we perform a thorough, large-scale evaluation of methods for activity recognition and fall detection on four datasets. On the first two we showed that the left wrist performs better compared to the dominant right one, and also better compared to the elbow and the chest, but worse compared to the ankle, knee and belt. On the third (Opportunity) dataset, our method outperformed the related work, indicating that our feature-preprocessing creates better input data. And finally, on a real-life unlabeled dataset the recognized activities captured the subject's daily rhythm and activities. Our fall-detection method detected all of the fast falls and minimized the false positives, achieving 85% accuracy on the first dataset. Because the other datasets did not contain fall events, only false positives were evaluated, resulting in 9 for the second, 1 for the third and 15 for the real-life dataset (57 days data). [ABSTRACT FROM AUTHOR]