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Unformatted text preview: Math 137 Week 7 Notes – Dr. Paula Smith 3.7 Word problems are the intersection of math learning with real-world applications. In general, when dealing with word problems: • Read the problem carefully. • Write down what you are given, and what you are to find out. • Sketch the situation and introduce notation. • Devise an equation that satisfies the situation. • Solve the equation. • Reinterpret the answer in terms of the original problem. In this section, the key is to use differentiation to solve the problem. In general, words that signal that you are to use differentiations include: Slope, rate, rate of change, rate of change of (variable 1) with respect to (variable 2), instantaneous rate of change, speed, velocity (derivative of distance, height, position), acceleration (derivative of velocity), current (derivative of charge), marginal cost (derivative of cost with respect to quantity), marginal revenue (derivative of revenue with respect to quantity), rate of growth, “how fast is _____ changing/increasing/decreasing.” Very often when only the word “rate” is used, the derivative is with respect to time. Very often when only the word “rate” is used, the derivative is with respect to time....
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This note was uploaded on 04/13/2010 for the course MATH 137 taught by Professor Speziale during the Spring '08 term at Waterloo.
- Spring '08