Math Help - Cont. Proof

1. Cont. Proof

prove if $f,g$ are cont. on $[a,b]$, if $f(a) < g(a), f(b) > g(b)$, then there is a $c \in [a,b]$ s.t. $f(c) = g(c)$.

Ok so I believe I need to prove this using the Intermediate Value Thm. Do I need to apply the IVT to f - g? If that's even a correct approach, how do I begin to do that?

2. Originally Posted by Math2010
prove if $f,g$ are cont. on $[a,b]$, if $f(a) < g(a), f(b) > g(b)$, then there is a $c \in [a,b]$ s.t. $f(c) = g(c)$.
Define $h(x)=f(x)-g(x)$ then $h(a)<0~\&~h(b)>0$.