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Suppose that f(x) is continuous in [0, 1...

Suppose that f(x) is continuous in [0, 1] and `f(0) = 0, f(1) = 0`. Prove `f(c) = 1 - 2c^(2)` for some `c in (0, 1)`

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`rArr" "f(c) = 1 - 2c^(2)`
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