Explanation

Intermediate Value Theorem (IVT):
If f(x) is continuous on [a,b] and f(a) ≠ f(b), then for any value L between f(a) and f(b), there exists c ∈ (a,b) where f(c) = L

Example:
f(x) = x³, f(1)=1, f(2)=8 → there is c where f(c)=5

Quiz

1. What does IVT require?

2. Does function need to be continuous?

3. What interval?

4. f(0)=2, f(3)=5, L=4 → exists c?

5. Can IVT find roots?

Answer Key

1. Continuous function on [a,b]

2. Yes

3. [a,b]

4. Yes

5. Yes