Thread: Intermediate Value Theorem

Can somebody help me with this problem. I'm trying to just understand it but having a hard time. Thanks

Use the Intermediate Value Theorem to show that there is a root of the equation x3+2x2=42 on the interval (0, 3). Your final answer should state your chosen values of N, f(x), a, and b.

IVT: If f is continuous on the interval and is a number between and , then there exists a number in the interval such that

For your question, imagine s = 0 (i.e. a root)

Let . Note: and . So what can you conclude from IVT?

So anything in between these two points 0 and 3 on the X-axis which will be C, will equal automatically equal S, which is between F(a) and F(b)?

The theorem says that if you give me a number between f(0) and f(3), call it s, I can guarantee you that I will find you a number c in between 0 and 3 such that f(c) = s.

Put s = 0 and you're done.