Practice Application: Optimization Problem (6) - Maxima and Minima - IB 10 Mathematics

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the area function for a rectangle with a perimeter of 20 cm?
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Express the area in terms of one variable.
Question 2.
What is the first derivative of A(x) = 10x - x²?
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Differentiate the area function.
3Question 3.
What is the first step in solving an optimization problem?
- Set the area function
- Identify the perimeter
- Find the length and width
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Remember the formula for area.
4Question 4.
True or False: Critical points occur where the first derivative is zero.
- True
- False
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Recall the definition of critical points.
Question 5.
A farmer has 100 meters of fencing to create a rectangular enclosure. How can they optimize the area? What dimensions will maximize the area?
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Use the same methods as we practiced; don’t forget to relate perimeter to length and width.
Question 6.
You want to design a rectangular billboard with a fixed perimeter of 90 meters to maximize visible area. What dimensions will you choose?
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Remember to express the area in terms of a single variable.

4 more questions in this section. Enroll free to practise them all.