# Math Help - One Question In Real Analysis ..

1. ## One Question In Real Analysis ..

Hi all..

"suppose that f continuous on [a,b] , that f(x) >= 0 (more or equal 0 ) for all x in [a,b] and that =0

prove that f(x)=0 for all x in [a,b] "

2. Suppose $\exists c \in [a,b]$ such that $f(c) > 0$. Then there exists a neighborhood $N$ of $c$ such that $f(x)>f(c)/2$ for all $x \in N \cap [a,b]$. (Prove this using the continuity of $f$ at $c$.) Then $0 = \int_a^b f \geq \int_{N \cap [a,b]} f(c)/2 > 0$ which is false.