# Intermediate Value Theorem

• Sep 8th 2008, 04:17 PM
Afterme
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.
• Sep 8th 2008, 04:29 PM
o_O
IVT: If f is continuous on the interval \$\displaystyle [a,b]\$ and \$\displaystyle s\$ is a number between \$\displaystyle f(a)\$ and \$\displaystyle f(b)\$, then there exists a number \$\displaystyle c\$ in the interval \$\displaystyle [a,b]\$ such that \$\displaystyle f(c) = s\$

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

Let \$\displaystyle f(x) = x^3 + 2x^2 - 42\$. Note: \$\displaystyle f(0) = -42\$ and \$\displaystyle f(3) = 444\$. So what can you conclude from IVT?
• Sep 8th 2008, 05:29 PM
Afterme
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)?
• Sep 8th 2008, 07:48 PM
o_O
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.