Serverless functions are a cloud computing paradigm where the provider takes care of resource management tasks such as resource provisioning, deployment, and auto-scaling. The only resource management task that developers are still in charge of is selecting how much resources are allocated to each worker instance. However, selecting the optimal size of serverless functions is quite challenging, so developers often neglect it despite its significant cost and performance benefits. Existing approaches aiming to automate serverless functions resource sizing require dedicated performance tests, which are time-consuming to implement and maintain. In this paper, we introduce an approach to predict the optimal resource size of a serverless function using monitoring data from a single resource size. As our approach does not require dedicated performance tests, it enables cloud providers to implement resource sizing on a platform level and automate the last resource management task associated with serverless functions. We evaluate our approach on three different serverless applications, where it selects the optimal memory size for 71.7% of the serverless functions and the second-best memory size for 22.3% of the serverless functions, which results in an average speedup of 43.6% while simultaneously decreasing average costs by 10.2%.