A taste of calculus 1 problems for math majors!

Let f be a continuous function on [0, 1] and f(0)=f(1). Show that, for n=2, 3, 4, ..., there is some a in [0, 1-1/n] such that f(a)=f(a+1/n). Learn how to use the Intermediate Value Theorem to prove the above statement. This question appears on the transfer entrance exam at National Taiwan Univiersity: https://exam.lib.ntu.edu.tw/sites/default/files/exam/undergra/102/102018.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