Alzheimer's disease (AD) is an irreversible brain disease that can dramatically reduce quality of life, most commonly manifesting in older adults and eventually leading to the need for full-time care. Early detection is fundamental to slowing its progression; however, diagnosis can be expensive, time-consuming, and invasive. In this work we develop a neural model based on a CNN-LSTM architecture that learns to detect AD and related dementias using targeted and implicitly-learned features from conversational transcripts. Our approach establishes the new state of the art on the DementiaBank dataset, achieving an F1 score of 0.929 when classifying participants into AD and control groups.