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3. Let f : R R be a continuously differentiable function and let f'(-) denote the derivative of f. Using only the definitions/theorems we discussed

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3. Let f : R R be a continuously differentiable function and let f'(-) denote the derivative of f. Using only the definitions/theorems we discussed in class, prove that: a. If f'(x) > 0 then f is increasing in a neighborhood around x (5 pts) b. If f'(x)

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