Unformatted text preview: f ( x ) = 0 for x ∈ [ a, b ]. 3. Let f, g : [ a, b ] → R . Suppose that f is di±erentiable and nondecreasing on [ a, b ], and f ′ is continuous on [ a, b ], and that g is di±erentiable 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...
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 Winter '07
 Fukuda
 Calculus, Derivative, dx

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