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(Solution) - Assume that f and g continuous functionals on a b -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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Assume that f and g continuous functionals on [a, b] ? ? that are differentiable on the open interval (a, b). Then there exists some x ? (a, b) such that

Assume that f and g continuous functionals on [a, b]
Provided g(a) ? g(b) and g?(x) ? 0, this can be written as
Assume that f and g continuous functionals on [a, b]

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