My Favorite One-Liners: Part 72

In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

In calculus, the Intermediate Value Theorem states that if f is a continuous function on the closed interval [a,b] and y_0 is any number between f(a) and f(b), then there is at least one point c \in [a,b] so that $f(c) =y_0$.

When I first teach this, I’ll draw some kind of crude diagram on the board:

In this picture, f(a) is less than y_0 while f(b) is greater than y_0. Hence the one-liner:

I call the Intermediate Value Theorem the Goldilocks principle. After all, f(a) is too low, and f(b) is too high, but there is some point in between that is just right.

 

 

 

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