Optimization problem are all about realizing the best possible outcome in a situation, subject to a identify the absolute maximum or minimumAKAST SELE OUTCO derivative equ can can occur at the endpoints of an interval, or at points for which 1. Draw a diagram label variables and constants. 2. Define: Ovanables (with units) quantity to be maximized or minimized (with units). 3. Write a fonction for the quantity and define a closed interval for the function. 4. Differentiate the function. 3. Let dy - and solve Use PDT. 6. Find the y-coordinates for the endpoints of the interval value that make - Contical valves) 7. Therefore statemenil. Ex. 1 Three sides of a rectangular field fenced in with 400 m offencing. Find the dimensions x x Let x represent the width of the enclosure, in metres, x70 Lety represent the length of the enclosure, in metres, yoo. P=2x+y₁ 400=2x+y 400-2x=4 A= xy. Subin A= x(400-2x) = 400x-2x² dA όχι 400-47 set dA-O όχ 0=400-4 FDT 100 = x fox) fox) αA Interval Solh Ford ax 14100 + > x=100 N/A max. 07100 - <0 Sub x=100 to ①. y=400-2(100) = 00 the dimensions of the rectangle would be The tensile strength of a new plastic at temperature T (°C) is given by the relationship S = ln(T+500) - 4T + 2100, where S represents the tensile strength measured in megapascals (MPa). Determine the temperature at which the tensile strength is a maximum.
Optimization problem are all about realizing the best possible outcome in a situation, subject to a identify the absolute maximum or minimumAKAST SELE OUTCO derivative equ can can occur at the endpoints of an interval, or at points for which 1. Draw a diagram label variables and constants. 2. Define: Ovanables (with units) quantity to be maximized or minimized (with units). 3. Write a fonction for the quantity and define a closed interval for the function. 4. Differentiate the function. 3. Let dy - and solve Use PDT. 6. Find the y-coordinates for the endpoints of the interval value that make - Contical valves) 7. Therefore statemenil. Ex. 1 Three sides of a rectangular field fenced in with 400 m offencing. Find the dimensions x x Let x represent the width of the enclosure, in metres, x70 Lety represent the length of the enclosure, in metres, yoo. P=2x+y₁ 400=2x+y 400-2x=4 A= xy. Subin A= x(400-2x) = 400x-2x² dA όχι 400-47 set dA-O όχ 0=400-4 FDT 100 = x fox) fox) αA Interval Solh Ford ax 14100 + > x=100 N/A max. 07100 - <0 Sub x=100 to ①. y=400-2(100) = 00 the dimensions of the rectangle would be The tensile strength of a new plastic at temperature T (°C) is given by the relationship S = ln(T+500) - 4T + 2100, where S represents the tensile strength measured in megapascals (MPa). Determine the temperature at which the tensile strength is a maximum.
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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(This is a calculus optimization problem, please show all work and add the chart for the first derivative test just like this example I am giving here, do the work like the example and put that chart too)
Transcribed Image Text:Optimization problem are all about realizing the best possible outcome in a situation, subject to a
identify the absolute maximum or minimumAKAST
SELE OUTCO
derivative equ
can
can occur at the endpoints of an interval, or at points for which
1. Draw a diagram label variables and constants.
2. Define: Ovanables (with units) quantity to
be maximized or minimized (with units).
3. Write a fonction for the quantity and define a
closed interval for the function.
4. Differentiate the function.
3. Let dy - and solve Use PDT.
6. Find the y-coordinates for the endpoints of the
interval value that make - Contical valves)
7. Therefore statemenil.
Ex. 1 Three sides of a rectangular field
fenced in with 400 m offencing. Find the dimensions
x
x
Let x represent the width of the enclosure, in metres, x70
Lety represent the length of the enclosure, in metres, yoo.
P=2x+y₁
400=2x+y
400-2x=4
A= xy.
Subin
A= x(400-2x)
= 400x-2x²
dA
όχι
400-47
set dA-O
όχ
0=400-4
FDT
100 = x
fox)
fox)
αA
Interval
Solh
Ford
ax
14100
+
>
x=100
N/A
max.
07100
-
<0
Sub x=100 to ①.
y=400-2(100)
= 00
the dimensions of the rectangle would be
Transcribed Image Text:The tensile strength of a new plastic at temperature T (°C) is given by the relationship
S = ln(T+500) - 4T + 2100, where S represents the tensile strength
measured in megapascals (MPa). Determine the temperature at which the tensile strength is a
maximum.
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