Practice Optimization Problems (3.6.3) - Calculus

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6 sample questions

Question 1.
What is an optimization problem?
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Think about where you're looking for best results among several options.
Question 2.
Define critical point.
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Consider where the slope of the function could change direction.
3Question 3.
What is the first step in solving an optimization problem?
- Identify constraints
- Find the derivative
- Graph the function
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Think about what you need to do to monitor change.
4Question 4.
True or False: The second derivative can provide information about the concavity of a function.
- True
- False
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Consider how the graph bends.
Question 5.
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.
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Consider the relationship between length and width carefully.
Question 6.
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.
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Ensure you're applying what you've learned about profit calculations.

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