Let
be two continuous functions such that
Prove that there exists c ∈ [ a , b ] {\displaystyle {}c\in [a,b]} such that 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)
such that
.
