1. Sketch a derivative. Given a graph, sketch its instantaneous rate of change.
2. Analytical and Numerical approximation. Given an equation of the velocity travelled by an airplane as a function of time, find the instantaneous rate of change at t=a using analytical (use the definition of the derivative) and numerical analysis.
3. Solving difficult derivatives involving chain rule, ln, and trigonometric functions. Given a function that describes the position of a roller coaster as function of time, find the velocity at a specific interval of time.
4. Implicit Differentiation. At the instant that two cars, A travelling from west to east at 5 miles of the intersection point and B travelling from east to west at 7 miles of the intersection point a police man standing at this point measures the instantaneous rate of change when car A travels at 70mph and car B at 45mph. What will it be?
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Andrea,
This looks like a great start. Your plan encompasses the various ways to understand and work with derivatives.
If I were to trim any area I would cut back on section 3. Use the rollercoaster as an example that depicts those fundamental concepts. Don't worry about showing all the formulas for the 6 trig functions, the ln, e^x, inverse trig. Just be sure that the expression that you use is realistic for a rollercoaster.
Good luck and keep working. This will take a while.
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