Final answer:
Broca's area directs muscle movements involved in speech, located in the frontal lobe of the left hemisphere of the brain.
Step-by-step explanation:
The part of the cerebral cortex that directs the muscle movements involved in speech is known as Broca's area. This region is located in the frontal lobe of the brain, anterior to the primary motor cortex. Broca's area is associated with the motor commands necessary for the articulation of speech and is typically found in the left hemisphere of the brain, which is responsible for language in about 95% of the population. It is named after the French surgeon Paul Broca, who studied patients with speech production difficulties, implying a connection to this specific cortical region.