Practice Application Of Maxima And Minima In Real-life Problems (5) - Application of Calculus

Practice: Application of Maxima and Minima in Real-Life Problems

Lesson 5Application of Calculus

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8 questions

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3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the formula for the area of a rectangle?
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Think about the basic formula for area in geometry.
Question 2.
If a rectangle has a perimeter of 12, what could be one possible pair of dimensions?
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Remember the perimeter formula: 2(length + breadth).
3Question 3.
What technique do we use to find maxima and minima?
- Graph analysis
- First and second derivative tests
- Trial and error
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Think about how calculus helps analyze functions.
4Question 4.
True or False: A rectangle with a fixed perimeter cannot be a square if it maximizes area.
- True
- False
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Consider properties of squares versus rectangles.
Question 5.
A box with a square base is to be made with a surface area of 600 cm^2. What are the dimensions of the box that maximize its volume?
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Draw out the problem, label dimensions, and set your equations.
Question 6.
How would you optimize a rectangular garden using 20 m of fencing to maximize area, and what would be its dimensions?
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Ensure the total length of fencing is accounted for in your calculations.

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