Step 1: Understand the actions involved. Extending the thigh at the hip means moving the thigh backward, while flexing the knee means bending the knee joint.
Step 2: Identify the muscle groups listed and their primary functions. For example, the Iliopsoas primarily flexes the thigh at the hip, the Quadriceps femoris primarily extends the knee, and the Gluteus medius and minimus primarily abduct and medially rotate the thigh.
Step 3: Recall that the Hamstrings group (biceps femoris, semitendinosus, semimembranosus) is unique because it crosses both the hip and knee joints, allowing it to extend the thigh at the hip and flex the knee simultaneously.
Step 4: Match the muscle group to the described actions. Since the Hamstrings extend the thigh and flex the knee, they fit the problem's criteria.
Step 5: Conclude that the Hamstrings are the primary muscle group responsible for extending the thigh at the hip and flexing the knee.