The first calculus question on a National Taiwan University entrance exam (for transfers)

Let's tackle the first calculus question on a National Taiwan University transfer entrance exam. We have f and g being differential functions and d/dx(f(x))=-g(x) and d/dx(xg(x))=xf(x) and we'll show that f and g have "interlacing zeroes". Try the rest of the exam here https://www.lib.ntu.edu.tw/exam/undergra/98/98018.pdf 🛍 Shop my math t-shirts & hoodies: 👉 https://amzn.to/3qBeuw6 👉 Support this channel and get more content https://www.patreon.com/blackpenredpen #blackpenredpen #calculus