According to the PMBOKĀ® Guide and the Standard for Project Management, the project charter is developed within the Project Integration Management Knowledge Area. Specifically, this occurs during the Develop Project Charter process, which is the very first process in the Initiating Process Group.
As per PMI standards, Project Integration Management includes the processes and activities to identify, define, combine, unify, and coordinate the various processes and project management activities. The Project Charter is a critical element of this Knowledge Area because:
Authorization: It is the document issued by the project initiator or sponsor that formally authorizes the existence of a project and provides the project manager with the authority to apply organizational resources to project activities.
Alignment: It establishes a direct link between the project and the strategic objectives of the organization.
High-Level Boundaries: It documents high-level information such as the project purpose, measurable objectives, high-level requirements, overall project risk, and summary milestone schedule.
The other options are incorrect based on the following PMI Knowledge Area definitions:
Project Cost Management: This Knowledge Area is concerned with planning, estimating, budgeting, financing, funding, managing, and controlling costs so that the project can be completed within the approved budget. It uses the charter as an input, but does not create it.
Project Scope Management: This area focuses on ensuring the project includes all the work required, and only the work required. Like Cost Management, it uses the high-level boundaries defined in the charter to begin the Plan Scope Management and Collect Requirements processes.
Project Time Management: (Now referred to as Project Schedule Management) This area focuses on the timely completion of the project. It relies on the summary milestone schedule found in the project charter to develop the detailed schedule.
As per the PMI Lexicon of Project Management Terms, the Develop Project Charter process is essential for ensuring that the project manager and the performing organization are officially recognized and empowered to begin the planning phase.