we need to enclose o field with a rectangular fence.we have SO0 feer of fecing material and a building is onone side of the field and it won't need ang fencing alang that side.Determine he climensions of the fence that will enclose Hhe largest (maximum) are a.JUstify why it's a maximum Using the first or second derivative test.

Given: To enclose a field with a rectangular fence. We have 500 feet of fencing material…

we need to endlose o field ith a rectangular fence. we have 500 feer of fencing material and a building is on one side of the field and it won't need ang fencing along that side. Detemine tne climensions of the fence that will enclose the largest (maximum) area. JUstify why it's a maximum Using the first or second derivative test.

we need to endlose o field ith a rectangular fence. we have 500 feer of fencing material and a building is on one side of the field and it won't need ang fencing along that side. Detemine tne climensions of the fence that will enclose the largest (maximum) area. JUstify why it's a maximum Using the first or second derivative test.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 3SE: How are the absolute maximum and minimum similar to and different from the local extrema?

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Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.

Question

we need to enclose o field with a rectangular fence.
we have SO0 feer of fecing material and a building is on
one side of the field and it won't need ang fencing alang that side.
Determine he climensions of the fence that will enclose Hhe largest (maximum) are a.
JUstify why it's a maximum Using the first or second derivative test.

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