Question

2. The Derivative. No surprise here. Be able to discuss tangent and secant lines, the difference quotient, instantaneous vs. average rates of change, local linearity and zooming, and how they are all related (including the limiting process). Below are a few possible essay questions for the final exam. I can guarantee at least one and possibly up to three questions related to the concepts below will be on the final exam. I suggest that you try writing out essays to several of the questions and then have a fellow student read them to see whether they are clearly expressed, mathematically correct, and whether or not they fully answer the questions Possible short essay question: 1. Explain the relationship between average rate of change of a function and the instantaneous rate of change of a function at a point. Your explanation should include the correct use of the terms difference quotient and derivative, and your explanation should be illustrated with diagrams 2. The Derivative. No surprise here. Be able to discuss tangent and secant lines, the difference quotient, instantaneous vs. average rates of change, local linearity and zooming, and how they are all related (including the limiting process) 3. What is a continuous function? What is a differentiable function? Can a function be differentiable and not continuous? Can a function be continuous and not be differentiable? Provide some examples to illustrate the ideas

Answer 1

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