THEOREM OF THE DAY: The Intermediate Value Theorem

Theorem

Let $f(x)$ be a real-valued function which is continuous on the closed interval $[a, b]$ and such that $f(a) < f(b)$. Then for any value $y_0$ satisfying $f(a) < y_0 < f(b)$, there is a value $x_0$ satisfying $a < x_0 < b$ for which $f(x_0) = y_0$.

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