3.6.3 - Optimization Problems
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Practice Questions
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What is an optimization problem?
💡 Hint: Think about where you're looking for best results among several options.
Define critical point.
💡 Hint: Consider where the slope of the function could change direction.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the first step in solving an optimization problem?
💡 Hint: Think about what you need to do to monitor change.
True or False: The second derivative can provide information about the concavity of a function.
💡 Hint: Consider how the graph bends.
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Challenge Problems
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A farmer has 100 meters of fencing to create a rectangular enclosure. Express the area A as a function of width x, and find the dimensions that maximize the area.
💡 Hint: Consider the relationship between length and width carefully.
Suppose you are tasked with maximizing profit described by the function P(x) = 5x - x^2 where x is the quantity sold. Calculate the optimal quantity for maximum profit.
💡 Hint: Ensure you're applying what you've learned about profit calculations.
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