In Computer Science the most popular algorithms are searching and sorting algorithms. Finding a maximum element from the given vector is the most common application in any domain. To find a maximum element from the vector various strategies can be applied and various languages supports different built-in functions for the same operation. To find a maximum element in a language generally max() function is implemented, which can be invoked by importing modules in a particular script/ code, which will make easier for an programmer to implement. In contrast using linear search to find a maximum element in a vector needs deep understanding of an algorithm and implementation methodologies. This manuscript presents a comparative case study of the built-in function max() approach and the linear search method to find an element from the given vector. It analyzes their working principles, performance, computational complexity, and practical usability.