The second midterm is on Monday, October 20, during the regular class period.
The following is a chapter by chapter guide intended to help you organize the material we have covered as you study for your exam. It is only intended to serve as a guideline, and may not explicitly mention everything that you need to study. While this exam will not explicitly test chapters that are not included below, it is still a good idea to review what we have learned about functions and limits, since these ideas are heavily used in the listed chapters.
Please start by taking a look at class notes and the material that we discussed in class. Then review all relevant textbook sections and homework problems for the chapters given below, and make sure you can solve all of them. I have also compiled a list of additional practice problems, and solutions for the practice worksheet.
2.1 & 2.2: Know the difference between an average rate of change and an instantaneous rate of change, both algebraically and graphically. You should also understand the derivative of a function at a point as the instantaneous rate of change at that point and be able to compute it exactly, or estimate it from a graph or table of values.
2.3 & 2.4: Understand what we mean by the derivative function of a given function, and be able to describe its behaviour using a graph or a table of numerical values. (This includes being able to draw the graph of the derivative.) You should also know the limit definition of the derivative function and use it to get a formula for the derivative. Finally, you should be able to recognize situations in which it is appropriate to use the derivative to model a slope or rate of change, carry out these computations, and determine the units for the derivative in those cases.
2.5: Know what we mean by the second derivative and how to compute it by finding the derivative of a derivative. You should also be able to interpret it graphically by relating it to the concavity of the graph of a function. You must also know the terms velocity and acceleration, and how they relate to the first and second derivatives of position given as a function of time.
2.6: You should know what it means for a function to be differentiable, and recognize graphically and algebraically when a limit does or does not exist. Remember that a differentiable function is continuous, but a continuous function is not always differentiable.
3.1 & 3.2: Know the derivatives of powers of x and exponential functions. Also know the rules for finding the derivative of a constant multiple of a function and the derivative of the sum of different functions.
3.3 & 3.4: You must certainly know the product rule and chain rule and be able to determine when it is appropriate to use these rules. You should also know the quotient rule, although you are welcome to use the product rule and chain rule to solve problems that could also be solved by the quotient rule.
3.5: You should know the derivatives of sin(x) and cos(x). You should know how to find the derivatives of the other trig functions, including tan(x), sec(x), csc(x) and cot(x).
3.6: You should know the derivative of ln(x).
Maintained by ynaqvi and last modified 10/17/14