Applications of Intermediate Value Theorem
Various applications of the Intermediate Value Theorem are discussed as follows:
- The theorem can be used to check the existence of roots of a continuous function in a specified interval.
- The theorem helps to check whether a continuous function attains a given value in a defined interval.
- The theorem is used in solving equations through numerical methods such as Bisection Method.
- The theorem serves as a base for proving several other theorems in calculus such as Mean Value Theorem.
- The theorem is also used to find critical points, i.e. points where the derivative of the function attains a specific value.
Intermediate Value Theorem
Intermediate Value Theorem is a theorem in calculus which defines an important property of continuous functions. It is abbreviated as IVT. The theorem is quite intuitive one but provides a significant result for the interpretation of the behaviour of functions. It can be used to know the range of values for a physical quantity such as temperature if an expression in terms of time or other variables is known for it. Other applications of the theorem include solving equations, proving the existence of roots, and analyzing real-world problems where continuity is observed.
In this article, we will learn the statement of the theorem, its proof by two different approaches, its various applications, the converse of the theorem, some numerical problems and related frequently asked questions.
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