How to use the Intermediate Value Theorem (KristaKingMath)

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The Intermediate Value Theorem is a continuity theorem that allows you to prove that a function has at least one solution or root in a given interval. Oftentimes it's used to show that a graph crosses the x-axis within a specific interval.

You can use the theorem with either a closed or open interval, but a closed interval is more common.

In order to use the Intermediate Value Theorem, the function has to be continuous (and therefore differentiable) on the interval, including at each endpoint. If this condition is met, and you can choose a value along the y-axis that lies between the values of the function at the endpoints of the given interval, then the Intermediate Value Theorem guarantees that there is a point within the interval that will result in the value you picked when you evaluate the function at the point within the interval.

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