Let f {\displaystyle {}f} be a Riemann-integrable function on [ a , b ] {\displaystyle {}[a,b]} with
for all x ∈ [ a , b ] {\displaystyle {}x\in [a,b]} . Show that if f {\displaystyle {}f} is continuous at a point c ∈ [ a , b ] {\displaystyle {}c\in [a,b]} with f ( c ) > 0 {\displaystyle {}f(c)>0} , then
![{\displaystyle {}[a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8e5a6e660b5cdc1a9c76f6e6b0d486328c3f6937)
![{\displaystyle {}x\in [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fda0a4b129005203d4c9b056c7aa53a1bbbe2840)
![{\displaystyle {}c\in [a,b]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0e96620a8d7941d7b882a2148f8703b82848ecad)
