Question

You have 40 meters of fencing and would like to enclose a rectangle of the largest...

You have 40 meters of fencing and would like to enclose a rectangle of the largest possible area. What should the dimensions of this rectangle be? Use the second derivative test to show that this is actually a maximum, and not a minimum.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find the largest possible rectangular area you can enclose with 420 meters of fencing. What is...
Find the largest possible rectangular area you can enclose with 420 meters of fencing. What is the significance of the dimensions of this enclosure, in relation to geometric shapes?
paul has 400 yards of fencing to enclose a rectangular area. find the dimensions of the...
paul has 400 yards of fencing to enclose a rectangular area. find the dimensions of the rectangle that maximize that enclosed area. what is the maximum area?
I would like to create a rectangular vegetable patch. The fencing for the east and west...
I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. I have a budget of $128 for the project. What are the dimensions of the vegetable patch with the largest area I can enclose? north and south sides= ? east and west sides = ?
Farmer Ed has 7 000 meters of​ fencing, and wants to enclose a rectangular plot that...
Farmer Ed has 7 000 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, what is the largest area that can be​ enclosed?
I would like to create a rectangular vegetable patch. The fencing for the east and west...
I would like to create a rectangular vegetable patch. The fencing for the east and west sides costs $4 per foot, and the fencing for the north and south sides costs only $2 per foot. I have a budget of $176 for the project. What are the dimensions of the vegetable patch with the largest area I can enclose? HINT [See Example 2.]. North East sides = East and West sides =
the back of monique's property is a creek. Monique would like to enclose a rectangular area,...
the back of monique's property is a creek. Monique would like to enclose a rectangular area, using the creek as one side fencing for the other three sides to create a corral. If there is 620 feet of fencing available, what is the maximum possible area of the corral? answer in square feet
Consider the following problem: A farmer with 650 ft of fencing wants to enclose a rectangular...
Consider the following problem: A farmer with 650 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens? (a) Draw a diagram illustrating the general situation. Let x denote the length of each of two sides and three dividers. Let y denote the length of the other two sides. (b) Write an expression for...
A farmer has 420 feet of fencing to enclose 2 adjacent rectangular pig pens sharing a...
A farmer has 420 feet of fencing to enclose 2 adjacent rectangular pig pens sharing a common side. What dimensions should be used for each pig pen so that the enclosed area will be a maximum? The two adjacent pens have the same dimensions. Find the absolute maximum value of f(x)= x4−2x
A homeowner wants to create an enclosed rectangular patio area behind their home. They have 168...
A homeowner wants to create an enclosed rectangular patio area behind their home. They have 168 feet of fencing to use, and the side touching the home does not need fence. What should the dimensions of the patio be to enclose the largest area possible?
Consider the circle around the origin (0,0) with a radius of r=2. You may need to...
Consider the circle around the origin (0,0) with a radius of r=2. You may need to recall the equation defining such a circle. Our goal is to draw a rectangle inside the circle, but we'd like to draw the largest possible rectangle. Find the dimensions of the largest rectangle that would fit and make sure the dimensions give the maximum area possible.