The Intermediate Value Theorem is a popular concept in Calculus, often studied together with the mean value theorem. Here I will state the theorem and help you understand this with the help of the Intermediate Value Theorem calculator.

## Intermediate Value Theorem

Let f(x) be a function which is continuous on $[a, b]$, $N$ be a real number lying between $f(a)$ and $f(b)$, then there is at least one $c$ with $a \leq c \leq b$ such that $N = f(c)$.

The IVT is also known as Bolzano’s theorem and Weierstrass Intermediate Value Theorem by some mathematicians. Bolzano provided the first proof of the theorem, but at his time the nature of real numbers wasn’t well-defined. The detailed proof was later done by Karl Weierstrass.

The Weierstrass proof of the Intermediate Value Theorem can be found here.

See the definitions of

## Intermediate Value Theorem Calculator

* *Click on the button above to launch the Intermediate Value Theorem calculator and grapher. If the button doesn't appear then you are using an incompatible browser or your browser doesn't have proper Javascript support. Try opening this page in Google Chrome or any other modern browser. This works on mobile devices too.

Note: $x_{min}$ and $x_{max}$ are just graph plotting ranges. These don't have anything to do with the Intermediate Value Theorem. Increase or decrease the values to increase the graph size.

Also, see, mean value theorem calculator.

Need some books on calculus? See the list of the best Calculus Text Books.

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