# Possibly an intermediate value theorem proof, but I'm not sure.

• Jul 4th 2011, 08:59 AM
CountingPenguins
Possibly an intermediate value theorem proof, but I'm not sure.
Question:

Suppose that f:[a,b]→ℝ and g:[a,b]→ℝ are continuous functions such that f(a)≤g(a) and f(b)≥g(b). Prove that f(c)=g(c) for some c∈[a,b].

Intermediate value theorem? Pinching Theorem? I'm not sure on this one.
• Jul 4th 2011, 09:08 AM
Plato
Re: Possibly an intermediate value theorem proof, but I'm not sure.
Quote:

Originally Posted by CountingPenguins
Suppose that f:[a,b]→ℝ and g:[a,b]→ℝ are continuous functions such that f(a)≤g(a) and f(b)≥g(b). Prove that f(c)=g(c) for some c∈[a,b].

Use the Intermediate value theorem on $h(x)=g(x)-f(x).$