This preview shows page 1. Sign up to view the full content.
Unformatted text preview: f ( x ) = 0 for x [ a, b ]. 3. Let f, g : [ a, b ] R . Suppose that f is dierentiable and non-decreasing on [ a, b ], and f is continuous on [ a, b ], and that g is dierentiable on [ a, b ] and g is integrable on [ a, b ], and g is strictly positive on ( a, b ) but g ( a ) = g ( b ) = 0. Then, show that f is constant on [ a, b ] if and only if i b a f ( x ) g ( x ) dx = 0 . 1...
View Full Document
This homework help was uploaded on 04/08/2008 for the course MATH 125B taught by Professor Fukuda during the Winter '07 term at UC Davis.
- Winter '07