NEW: Olivia de Havilland: "I was shocked and saddened to learn of the passing of my sister"
Fontaine was a teenager when she began her acting career in 1935
She and sister Olivia de Havilland carried on a lifelong rivalry
She wrote in her autobiography that her mother encouraged the rivalry with her older sister
Oscar-winning actress Joan Fontaine died Sunday, her longtime friend Noel Beutel said Monday. She was 96.