Preliminary Remarks on the Determination of the Extrema of a Continuous Function of One Variable

Abstract

When one discusses the maximum and minimum of a function of one variable, it would be unwise to consider this problem as solved by the simple act of putting the derivative equal to zero. This procedure is often, but not always correct. Thus, one should proceed with the greatest caution, and investigate more closely the different kind of situations which can arise. We shall illustrate this graphically, and in doing this will provisionally accept a purely intuitive concept of the derivative, considered as the slope of the tangent.