<p>This article is the result of the reflections that, as a high school teacher, have emerged from noticing the students' clear difficulty regarding the calculus subject. It is consolidated a proposal focused on the analysis and determination of the solution to the equation problem of the tangent line to polynomial functions; this solution is extended to form functions&nbsp;f(x)= ax<sup>n&nbsp;</sup>&nbsp;, with&nbsp;n ε Q n ε Q&nbsp;and&nbsp;a&nbsp;ε R a&nbsp;ε R&nbsp;, by means of the so-called Caratheodory derivative; it is concluded with an alternative approximation that can also be object of study, even at elementary level.</p>