Alzheimer's disease is a global health challenge, emphasizing the need for early detection to enable timely intervention and improve outcomes. This study analyzes handwriting data from individuals with and without Alzheimer's to identify predictive features across copying, graphic and memory-based tasks. Machine learning models, including Random Forest, Bootstrap Aggregating (Bagging), Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), Adaptive Boosting (AdaBoost) and Gradient Boosting, were applied to classify patients, with SHapley Additive exPlanations (SHAP) enhancing model interpretability. Time-related features were crucial in copying and graphic tasks, reflecting cognitive processing speed, while pressure-related features were significant in memory tasks, indicating recall confidence. Simpler graphic tasks showed strong discriminatory power, aiding early detection. Performance metrics demonstrated model effectiveness: For memory tasks, Random Forest achieved the highest accuracy (