The second midterm is on Friday, November 7, 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, limits and derivatives, 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.
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), and more generally, loga(x). You should also be able to find the derivative of an inverse function given information about the derivative of the original function.
3.7: Know how to find the derivative of an implicitly defined variable by differentiating both sides of an equation with respect to the appropriate variable. Make sure you know how to use this method to find the derivatives of inverse trig functions, such as arcsin(x) and arccos(x).
3.9: Given a function, you should be able to find the equation of the tangent line to the graph at a given point. You should also be able to use this linearization to approximate values of the function near the given point, and determine whether this approximation is an overestimate or an underestimate using the concavity of the graph.
4.1 & 4.2: You should be able to use the derivative of a function to find all its critical points, and you should be able to classify each critical points as a local minimum, local maximum or inflection point. Finally, you should be able to find the global (ie, overall) maximum and minimum values of a function on a closed interval by looking at its values at critical points and endpoints.
Maintained by ynaqvi and last modified 11/01/14