Why the Buddha abandoned asceticism

It is commonly known that the Buddha decided that asceticism does not lead to enlightenment, but less common is the reason why given. From Ajahn Brahm's book Mindfulness, Bliss, and Beyond , it appears as though the Buddha abandoned asceticism because eating well was necessary to pursue the jhānas and the Middle Way: > once the Bodhisatta realized that jhāna was the way to enlightenment > (MN 36,31), he immediately recognized that it was impractical to > attain jhāna with an emaciated body so began eating well. Where in MN 36 do we find this reasoning? Is there general agreement in Buddhism that this is indeed why the Buddha decided to give up asceticism?