Let
be two continuous functions and let g ( t ) ≥ 0 {\displaystyle {}g(t)\geq 0} for all t ∈ [ a , b ] {\displaystyle {}t\in [a,b]} . Prove that there exists s ∈ [ a , b ] {\displaystyle {}s\in [a,b]} such that
![{\displaystyle f,g\colon [a,b]\longrightarrow \mathbb {R} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/62d73c59b59bcbf77e12fcb056dfc8687ee91d08)
![{\displaystyle {}t\in [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9c4aaf960a5aea5a6e51c3a6710b3a02caaecd2b)
![{\displaystyle {}s\in [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/23d79d7da8a05f246e9ae8886249848283918b3f)
