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A student solves an optimization problem as in Model 1, except that in the problem Mini and Max are given 800 feet of caution tape. Examine the student's solution, explain what they did wrong, and write down what the student should have done instead. Student Solution (find the error): A = xy P = 2x+2y = 800 400- x = y A = x (400-x) = 400 x - x² A'(x) = 400-2x, so x = 200 is a critical number. Check the endpoints (x = 0 and x = 400) and critical number: A'(0) = 400; A'(200) = 0; A'(400) = -400. Therefore the maximum area is 400 square feet.

A student solves an optimization problem as in Model 1, except that in the problem Mini and Max are given 800 feet of caution tape. Examine the student's solution, explain what they did wrong, and write down what the student should have done instead. Student Solution (find the error): A = xy P = 2x+2y = 800 400- x = y A = x (400-x) = 400 x - x² A'(x) = 400-2x, so x = 200 is a critical number. Check the endpoints (x = 0 and x = 400) and critical number: A'(0) = 400; A'(200) = 0; A'(400) = -400. Therefore the maximum area is 400 square feet.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A student solves an optimization problem as in Model 1, except that in the problem Mini and Max are given 800 feet of caution tape. Examine the student's solution, explain what they did wrong, and write down what the student should have done instead. Student Solution (find the error): A=xy P = 2x+2y = 800 400 - x = y A = x (400-x) = 400 x - x² A'(x) = 400 2x, so x = 200 is a critical number. Check the endpoints (x = 0 and x = 400) and critical number: A'(0) = 400; A'(200) = 0; A'(400) = -400. Therefore the maximum area is 400 square feet.
Transcribed Image Text:A student solves an optimization problem as in Model 1, except that in the problem Mini and Max are given 800 feet of caution tape. Examine the student's solution, explain what they did wrong, and write down what the student should have done instead. Student Solution (find the error): A=xy P = 2x+2y = 800 400 - x = y A = x (400-x) = 400 x - x² A'(x) = 400 2x, so x = 200 is a critical number. Check the endpoints (x = 0 and x = 400) and critical number: A'(0) = 400; A'(200) = 0; A'(400) = -400. Therefore the maximum area is 400 square feet.
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