Test 2 covers the following objectives:
Sections 3.1 & 3.2
- State, explain, and illustrate the limit definition of derivative.
- Use the limit definition of derivative to evaluate a derivative.
- Interpret the derivative as the slope of a tangent line.
- Find equations of tangent lines.
- Determine when a derivative does not exist.
- Graph the derivative function from the graph of a given function.
- Evaluate derivatives (and higher-order derivatives) using basic
- Calculate an average rate of change (i.e., slope of a secant
- Interpret the derivative as an instantaneous rate of change.
- Solve problems involving motion along a line.
- Solve various application problems involving rates of change.
- Evaluate derivatives of trigonometric functions.
- Identify compositions of functions, and write a function as a
composition of two functions.
- Use the chain rule to differentiate compositions of functions.
- Use implicit differentiation to find the derivative of an implicitly-defined function.
- Find equations of the lines tangent and normal to the graph of an implicitly-defined function.
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