Category: Exam Review (Page 1 of 2)

The final exam for the course will be on Tuesday (Dec 20), during our usual class time.

Listed below is a list of topics and exercises to review in preparation for the exam. I have uploaded solutions to the midterm exams to OpenLab Files. I recommend downloading the pdfs and studying the solutions as you review these topics:

• The limit definition of the derivative: Exam 1 (exercise #1), Exam 3 (#1)
• Finding the derivative of a given function using the differentiation rules: Exam 1 (#4), Exam 2 (#4), Exam 3 (#2), Quiz #2, Quiz #3
• Finding the equation of the tangent line for a given function at a given point (using the derivative and the point-slope equation of the line): Exam 1 (#3), Exam 2 (#3), Quiz #2
• Finding a linear approximation: Exam 3 (#3)
• Using the derivative as instantaneous rate of change: Exam 2 (#1 and #2)
• Using the derivative to find extrema and the shape of the graph (finding critical points and where the graph is increasing/decreasing): Exam 3 (#4)
• Applied optimization: WebWork “Application – Optimization” #1-3

The last midterm exam is a take-home exam. I will distribute it class today (I will also upload the pdf to OpenLab), and it will be due Tuesday (Dec 13) at the beginning of class.

I will update this post below with a list of WebWork exercises and textbook examples to review as you are working through the exam.

#1: finding the derivative of a function using the definition of the derivative: see Sec 3.2, Example 3.12

#2: finding derivatives using the derivative rules, derivatives of trig functions, and derivatives of exponential and logarithmic functions): see examples in Sections 3.3, 3.5, 3.6, 3.9

#3: (finding/using the “linearization” of a function at point: See Sec 4.2, WW “Application – Linearization”

#4: Finding critical points, local maxima/minima, intervals where function is increasing/decreasing: See Sec 4.3 and 4.5; WW “Application – Extrema” (#1-4), “Application – Montonicity” (#3), “Application – Shape of Polynomials” (#1-4)