The Intermediate Value Theorem
The Intermediate Value Theorem states if
f
is continuous on the closed interval [
a
,
b
]
and
k
is
any number
between
f(a)
and
f(b),
then there is at least one number
c
in [
a,b
] such that
f(c) = k
.
As a simple example of this theorem, consider a person’s heart rate. A person’s heartbeat when fear sets in is
a continuous function. Kiah’s heartbeat at 9.50, the begging of AP Chemistry, was a steady 45 beats per minute.
However, Kiah’s teacher walked over to Kiah’s desk and picked up his most loved possession, his baseball glove.
His heart rate quickly began to get faster. Kiah took action to get his glove back making his heart rate increase
even more. After a knock-down-drag-out fight, the teacher and Kiah both ended up on the ground, leaving the
teacher, and his pride, not only in embarrassment, but in outrage. Once the teacher shouted loudly at the entire
class to “call the authority” at 9:55, Kiah’s heart rate was at a maximum of 170 beats per minute. In this crazy,