Final answer:
A PET scan is the most appropriate test to confirm Alzheimer's disease as it can detect beta-amyloid plaques, which are indicative of Alzheimer's and are not shown in other imaging tests or cognitive assessments.
Step-by-step explanation:
To confirm the diagnosis of Alzheimer's disease in a 40-year-old woman with depression, the most appropriate investigation would be a Positron Emission Tomography (PET) scan. A PET scan is a highly effective imaging technique, especially useful in the diagnosis of Alzheimer's disease, as it can show the presence of beta-amyloid plaques in the brain. This is critical given that the main symptoms of Alzheimer's disease include memory loss, impaired movement, and cognitive decline, which can result from the growth of these plaques. While other options like an Electroencephalogram (EEG) could detect abnormal brain function and a Magnetic Resonance Imaging (MRI) could visualize brain atrophy, a PET scan is more specifically suited to identifying Alzheimer's pathology. The Mini-Mental State Examination (MMSE) is a cognitive screening tool that assesses mental status but does not confirm the diagnosis of Alzheimer's disease.