Intermediate Value Theorem. Objectives Students will be able to Determine if the Intermediate Value Theorem Applies to a particular function Use the Intermediate.

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Lesson 63 - Intermediate Value Theorem

Presentation transcript:

Intermediate Value Theorem

Objectives Students will be able to Determine if the Intermediate Value Theorem Applies to a particular function Use the Intermediate Value Theorem to determine if a function has a root on a given interval

Intermediate Value Theorem Let f(x) be continuous on a closed interval (one-sided continuity at the endpoints), and (we can say this without loss of generality). Then for any value d such that, there exists a value c such that and

Example 1 Use the Intermediate Value Theorem to determine if the equation below has a solution in the interval (0, 1).

Example 2 Use the Intermediate Value Theorem to determine if the function below has at least one root in the interval (-1, 1).

Example 3 The price of a gallon of gas at a particular QuickTrip was $2.61 on a Monday. The following Friday, the price of a gallon of gas was $2.75. Therefore, some time between that Monday and that Friday, there was a point where the piece of a gallon of gas was $2.70. Is the previous conclusion valid?