Consider a rectangle that has a perimeter of 40 inches. What are the dimensions (width and length) of the rectangle that would minimize the area? Use calculus techniques (section 4.6) to solve.
Consider a rectangle that has a perimeter of 40 inches. What are the dimensions (width and length) of the rectangle that would minimize the area? Use calculus techniques (section 4.6) to solve.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter5: Linear Inequalities
Section5.5: Solving Inequalities Involving Absolute Value
Problem 30PPS
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Consider a rectangle that has a perimeter of 40 inches. What are the dimensions (width and length) of the rectangle that would minimize the area? Use calculus techniques (section 4.6) to solve.
Transcribed Image Text:Solving Applied Optimization Problems
1. Read the problem. Read the problem until you understand it. What is given?
What is the unknown quantity to be optimized?
2. Draw a picture. Label any part that may be important to the problem.
3. Introduce variables. List every relation in the picture and in the problem as
an equation or algebraic expression, and identify the unknown variable.
4. Write an equation for the unknown quantity. If you can, express the unknown
as a function of a single variable or in two equations in two unknowns. This
may require considerable manipulation.
5. Test the critical points and endpoints in the domain of the unknown. Use
what you know about the shape of the function's graph. Use the first and
second derivatives to identify and classify the function's critical points.
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