View Intermediate Value Theorem Practice Problems Pictures. In mathematical analysis, the intermediate value theorem states that if f is a continuous function whose domain contains the interval a, b, then it takes on any given value between f(a) and f(b) at some point within the interval. We could change the above problem to make f(0.5) equal anything we want.

Mean Value Theorem from image.slidesharecdn.com

To work this problem, he uses the definition of the limit. The intermediate value theorem states that if a continuous function attains two values, it must also attain all values in between these two values. Even though the statement of the intermediate value theorem seems quite obvious, its proof is actually quite involved, and we have broken it down into.

Here we see a consequence of a function being continuous.

Suppose $f(x)$ is a continuous function on the interval $a,b$ with $f(a) \ne f(b)$. We have f (0) = 0 and f (−y) = 0. S \to \r$ be a real function on some subset $s$ of $\r$. However the c refers back to the c found in the function using the mean value theorem not just.