Get a preview of the work completed during a PLEM Academy Research Participation session. This video provides a short recap from Volume 6: Differential Calculus of the PLEM Crash Courses and demonstrates the type of mathematics, problem-solving methodology, and research preparation explored with participants.
The featured optimization problem asks: Find two positive numbers whose product is 100 and whose sum is a minimum. The recap examines how an optimization problem can be organized by identifying the necessary equations, using the given constraint to reduce a multivariable relationship to a single-variable function, differentiating that function, and determining its minimum.
The discussion also connects the algebraic solution to its graphical interpretation and demonstrates the use of the second derivative test to verify that the critical value produces a minimum. For this problem, the two positive numbers are 10 and 10, giving a minimum sum of 20.
PLEM Academy is designed as preparation and research participation—not as a replacement for your assigned coursework. Participants work on material outside their current courses, including subjects they may encounter in future semesters, while developing mathematical communication, research, textbook navigation, and systematic problem-solving skills.
This is a sample of the material developed through PLEM Academy Research Participation, where participants can take part in the ongoing development of mathematics and physics educational materials while gaining exposure to the way advanced STEM work is researched, organized, written, and communicated.