Mathematics 133 -- Calculus with Fundamentals 1

Exam 4 -- Things to Know

November 28, 2017

General Information

The fourth full-period exam of the semester will be given in class on Thursday, December 7. It will cover the material from sections 8,9,10 of Chapter 3 and sections 2,3,4,6, and 7 of Chapter 4. There will be eight or nine questions (maybe grouped together as parts of larger questions) similar to problems from the quizzes, problem sets, and in-class practice problems so far.

Tori will run a review session either Tuesday or Wednesday evening before the exam.

Material To Know

As you will have realized, almost all of the stuff from Chapters 1 and 2 and the first part of Chapter 3, especially things about piecewise-defined functions, operations on functions, various classes of functions, all of our techniques for computing limits, continuity, and techniques for computing derivatives (Sum, Product, Quotient, and Chain Rules) is relevant here too. In particular, you will need to be able to compute derivatives proficiently using combinations of these rules as needed. The new material not covered on the previous exams is:

• Section 3.8: Implicit differentiation -- know how to find dy/dx for the implicit functions y = y(x) defined by an xy-equation.
• Section 3.9: Derivatives of inverse functions -- specifically, the natural logarithm and the inverse sine and inverse tangent.
• Section 3.10: Related rates problems.
• Section 4.2: Extreme Values: This section includes using the critical points of a function, finding the absolute maximum and minimum values of a continuous function on a closed interval using the critical points.
• Section 4.3: The Mean Value Theorem and its consequences: If f'(x) is positive (respectively, negative, zero) on an interval, then f(x) is increasing (respectively, decreasing, constant) on that interval. The First Derivative Test for local maxima and minima.
• Sections 4.4 and 4.6: The second derivative and concavity. The Second Derivative Test for local maxima and local minima. Using information from the first and second derivatives (plus asymptotes) to sketch graphs of functions.
• Section 4.7: Applied optimization problems.

Good Review Problems:

Look at the Chapter 3 and Chapter 4 Review Problems from our book (with answers for the odd-numbered problems).

Also see the sample exam questions posted on the course homepage.