We investigate cubic intersections by moving plane, which depends on three parameters. For this we prove the main theorem and find the area function (Theorem 2). We show that the area function is a smooth function and differentiable once only. In many special cases this function has at least two points of maximum and four inflection points. For this purpose we also use computer-based methods. We recommend some special cases that can be used in school mathematics. In this way one can integrate together plane geometry, solid geometry, algebra, analysis and computer science.