Question: Minimum surface area box question: All boxes with a square base and a volume of 50 ft^3 have a surface area given by s(x)=2x^2+200/x, where

Minimum surface area box question:

All boxes with a square base and a volume of 50 ft^3 have a surface area given by s(x)=2x^2+200/x, where x is the length of the sides of the base. Find the absolute minimum of the surface area of a function. What are the dimensions of the box with minimum surface area? Please provide formulas and as much details on how to solve this problem.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

All boxes with a square base and a volume of 50 ft 3 have a surface area given by S(x) = 2x 2 + 200/x, where x is the length of the sides of the base. Find the absolute minimum of the surface area...

Show all work for the following Optimization problems. LPW - W W (1) Maximizing Area (i) Of all rectangles with a fixed perimeter of P feet, which one has the maximum area A? (Give the dimensions in...

3 5 6 . . . 4 . . . 200 . All boxes With a square base and a volume of 50 it3 have a surface area given by 5(37.) : 2:172 + , :r where .7: is the length of the sides of the base. Find the absolute...

4. [-/0.1 Points] DETAILS MY NOTES ASK YOUR TEA A closed rectangular box is to have a square base and a volume of 50 fts. Letting x denote the length of one side of the base, find a function fin the...

1. 200 All boxes with a square base, an open top, and a volume of 50 ft" have a surface area given by S(x) = x" + , where x is the length of the X sides of the base. Find the absolute minimum of the...

Suppose a tour guide has a bus that holds a maximum of 106 people. Assume his profit (in dollars) for taking n pec on a city tour is P(n)=n{53 - 0.5n) - 106_ {Although P is defined only for positive...

The distance in miles of a car from its starting point after t hours is given by the formulaf(t)=40t. (a) What is the average rate of change off(t)betweent=4andt=6 (b) What is the average rate of...

Help with this calc 1 question 160 All boxes with a square base, an open top, and a volume of 40 fto have a surface area given by S(x) = x + y , where x is the length of the sides of the base. Find...

What are some key differences between brazing and fusion welding?

What is frictional unemployment? Why is a certain amount of frictional unemployment probably necessary in a well-functioning economy?

What is a perpetuity? A perpetuity is an annuity with a life less than 1 0 years. A perp ? N Uuity is a stream of unequal payments that are received forever. A perpetuity is an unending stream of...

3. Wigwam Widgets started production on 250,000 widgets in March, with 160,000 completed. Material costs were $85,680 for the month while conversion costs amounted to $43,690. There was no beginning...