What type of authority does a principal give an agent in writing?

The correct answer is express warranty because an express warranty is a clear, definitive promise made by the principal, typically documented in writing, granting specific authority to the agent. This type of authority is directly communicated and identifiable through a written contract or an explicit statement, which dictates what the agent is permitted to do on behalf of the principal.

In contrast, other terms listed do not accurately describe the authority in question. Implied warranty usually refers to a guarantee that is not explicitly stated but understood to be part of the agreement—it's more about the quality or performance of a product than about granting authority. Customary authority refers to authority that is derived from the general practices in a particular industry, rather than from a specific written document. Apparent authority occurs when a third party believes an agent has authority based on the principal's representations, even if such authority has not formally been granted. Each of these options highlights different aspects of authority that do not fit the context of a formal, written directive from a principal to an agent.