Test 2 covers the following objectives:

Sections 3.1 & 3.2

  1. State, explain, and illustrate the limit definition of derivative.
  2. Use the limit definition of derivative to evaluate a derivative.
  3. Interpret the derivative as the slope of a tangent line.
  4. Find equations of tangent lines.
  5. Determine when a derivative does not exist.
  6. Graph the derivative function from the graph of a given function.

Section 3.3

  1. Evaluate derivatives (and higher-order derivatives) using basic differentiation rules.

Section 3.4

  1. Calculate an average rate of change (i.e., slope of a secant line).
  2. Interpret the derivative as an instantaneous rate of change.
  3. Solve problems involving motion along a line.
  4. Solve various application problems involving rates of change.

Section 3.5

  1. Evaluate derivatives of trigonometric functions.

Section 3.6

  1. Identify compositions of functions, and write a function as a composition of two functions.
  2. Use the chain rule to differentiate compositions of functions.

Section 3.8

  1. Use implicit differentiation to find the derivative of an implicitly-defined function.
  2. Find equations of the lines tangent and normal to the graph of an implicitly-defined function.

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