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1. Recall a definition of a function that we learned at the beginning of the course: A function is a rule that assigns one output to each input. If
1. Recall a definition of a function that we learned at the beginning of the course: A function is a rule that assigns one output to each input. If the derivative is a function, what are its inputs? What are its outputs?
2. Explain how a function could be continuous at a point but NOT differentiable at that point. Give examples.
3. If a function is differentiable at every point, is the function continuous? Explain.
4. Suppose you have a function f(x) . In your own words, explain what is meant by the notation f '(x) and how the two functions are related. (If the derivative is positive, what do we know about the original function? Why? What if the derivative is negative?)
