You need to be able to do the following:

• Find the equation for a tangent line (sec. 2.6 #7-10)
• Find the derivative of a function using the definition of a derivative (section 2.8 #19-25).
• Solve problems concerning velocity and/or rate of change (sec. 2.6 #14-25)
• Draw a rough sketch of f ‘(x) given the graph of f(x) (sec. 2.8 #1,2,4-11)
• Draw a rough sketch of f(x) given the graph of f ‘(x) (sec. 2.10 #1,2,11,12)
• Use a graph of f ‘(x) to determine on what intervals f(x) is increasing and decreasing, on what intervals f(x) is concave up and concave down, and where there are local maxima and minima (sec.2.10#3,11,12, 21,23,24
• Find just about any derivative using rules of differentiation (all of chapter 3)
• Differentiate a parametric curve (sec. 3.5#65-67)
• Use implicit differentiation to find the derivative of an implicit function (sec. 3.6)
• Use logarithmic differentiation to find derivatives of particularly complex functions (I will tell you when to use it) (sec.3.7 #27-36)

You will need to know and understand the following terms and concepts to successfully do the problems described above:

• Derivative at a point (p. 142)
• Concept of average rate of change vs. instantaneous rate of change (p. 146)
• The definition of a derivative (p. 150)
• Derivative as a slope (p. 151)
• Derivative as an instantaneous rate of change (pp. 152-153)
• Derivative as a function (sec. 2.8)
• Second derivative (p. 165)
• Increasing/decreasing on an interval (p. 175)
• Local maxima and local minima (p. 175)
• Concave up/concave down on an interval  (p. 176)
• Derivatives of basic functions (reference page 3 at back of book)
• Basic rules of differentiation (pp. 192-3)
• Product rule (p. 200)
• Quotient rule (p. 203)
• Chain rule (p. 225)
• Formula for derivatives of parametric equations (p. 231)
• Implicit differentiation (pp. 238-240; warning: the text is not very good at explaining implicit differentiation, but hopefully I will make up for that)
• Steps in logarithmic differentiation (p. 248)