<p>The derivation of necessary conditions of optimality for optimal control problems with state/control constraints is a challenging task, not always clearly understood. In this paper, we present a didactic approach based on the method of exponential penalty functions allowing, in our setting, to significantly simplify the proofs. This work may be viewed as a proposal of a course designed for students familiar with the basics of optimal control theory and elements of functional analysis. To make the analysis as simple as possible, we concentrate on the case of optimal control problem with fixed initial point and free end state.</p>