Let
be continuous functions with f ( a ) ≥ g ( a ) {\displaystyle {}f(a)\geq g(a)} and f ( b ) ≤ g ( b ) {\displaystyle {}f(b)\leq g(b)} . Show that there is a point c ∈ [ a , b ] {\displaystyle {}c\in [a,b]} with f ( c ) = g ( c ) {\displaystyle {}f(c)=g(c)} .
![{\displaystyle f,g\colon [a,b]\longrightarrow \mathbb {R} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/62d73c59b59bcbf77e12fcb056dfc8687ee91d08)
![{\displaystyle {}c\in [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0e96620a8d7941d7b882a2148f8703b82848ecad)
