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. $f(c) = g(c)$.
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 $h(a)<0~\&~h(b)>0$.