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 is a continuous function on the closed interval
and
is any number between
and
, then there is at least one point
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, is less than
while
is greater than
. Hence the one-liner:
I call the Intermediate Value Theorem the Goldilocks principle. After all,
is too low, and
is too high, but there is some point in between that is just right.
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