Intermediate Value Theorem
Friday, 15 March 2019
7:23 PM
Created with Microsoft OneNote 2016.
![Theorem. Let f (x) — x5 + '21 — 2. Then f (c) = 0 for some c e [0, 1].
2. Then f (0)
Proof. Let f (x) —
—2, which is negative, while
1, which is positive. Also f is continuous, as it is a polynomial. Therefore,
by the Intermediate Value Theorem, there exists a real number c strictly between
0 and 1 with f (c) = 0. This completes the proof.](Intermediate%20Value%20Theorem_files/image001.png)