This paper addresses the calculation of the extrema of the sin x/x fun
ction. First the Newton-Raphson method is used, which allows us to obt
ain the extrema locations very fast through the use of a recursion for
mula. Then a second approach is proposed, which gives the extrema loca
tions and the extrema amplitudes in the form of series expansions. Sim
ple, accurate algebraic expressions are derived.