Which medication is used for the treatment of epilepsy and bipolar disorder and is available by prescription?

Valproate is the correct choice as it is a medication that effectively treats both epilepsy and bipolar disorder, and it is only available by prescription. Valproate works by stabilizing electrical activity in the brain, making it beneficial for managing seizures. Additionally, it is utilized in treating the manic episodes of bipolar disorder due to its mood-stabilizing properties.

Carbamazepine is also a medication that treats epilepsy and is often used for bipolar disorder, but valproate is more commonly recognized for its broad effectiveness in both conditions. Lamotrigine is effective for bipolar disorder and epilepsy as well but is not as widely used as a first-line treatment for the manic episodes of bipolar disorder compared to valproate. Phenytoin is primarily used for epilepsy management and does not have a role in treating bipolar disorder, making it less relevant in this context.

In sum, among these options, valproate stands out for its dual efficacy in treating epilepsy and bipolar disorder.