1. If and , then has a local minimum at . 2. If a function has a local maximum at , then exists and is equal to 0. 3. If for all in , then is decreasing on . 4. A continuous function on a closed interval always attains a maximum and a minimum value. 5. . 6. Differentiable functions are always continuous. 7. If and are increasing on an interval , then is increasing on .
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