Parábolas versus logaritmos: intersecções

A very common question among university students is: Why study Calculus? Nowadays, even with all the current technologies, this question still becomes frequent, and its answer more complicated, since it is not always easy to clarify the connection between a given technology and the mathematics necessary to implement it. From the point of view of mathematics the situation is similar, it is not always easy to determine which mathematics is necessary to solve a given problem. In this article we present a problem about the intersection between parabolas and logarithms in which, in the geometric sense, the perception of the solution is quickly visualized, without the need to know mathematics. However, to show that this visual intuition coincides with the correct answer, one must necessarily consider the mathematics taught in Calculus courses. This opens space for discussions about the teaching of Calculus and also the differences between the mathematics seen in high school and the one seen in university.