
Optimization Calculus
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the formula for the area of a rectangle?
Back
The area (A) of a rectangle is calculated using the formula: A = length × width.
2.
FLASHCARD QUESTION
Front
What is the relationship between perimeter and area in rectangles?
Back
For a given perimeter, the rectangle with the maximum area is a square.
3.
FLASHCARD QUESTION
Front
How do you express the perimeter of a rectangle in terms of its length (l) and width (w)?
Back
The perimeter (P) of a rectangle is given by the formula: P = 2l + 2w.
4.
FLASHCARD QUESTION
Front
What is the maximum area of a rectangle with a fixed perimeter of 80 cm?
Back
The maximum area is achieved when the rectangle is a square, so the maximum area is 400 cm² (20 cm by 20 cm).
5.
FLASHCARD QUESTION
Front
How do you find the dimensions of a rectangle that maximize the area with a given amount of fencing?
Back
Set up the equation for the perimeter, express one variable in terms of the other, and then use calculus to find the maximum area.
6.
FLASHCARD QUESTION
Front
What is the significance of the first derivative in optimization problems?
Back
The first derivative helps identify critical points where the function may have maximum or minimum values.
7.
FLASHCARD QUESTION
Front
What does the second derivative test determine in optimization?
Back
The second derivative test determines whether a critical point is a local maximum, local minimum, or an inflection point.
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