Find a rectangular piece of paper, cardboard, poster-board, etc. to create a box. Measure the sides of your paper and record them below (if you are using a normal size piece of paper its dimensions are 8.5 inches by 11 inches). You will now have to determine the length, width, and height to make an open-top box with the maximum volume possible. To do this you will have to cut the corners of the paper to fold up (but don't do this yet). Assume the height of the box will be x, which means you will need to subtract x from both sides of the width and length. Use these three dimensions to create a volume equation which you can derive like we did yesterday to find the optimal value for x leading to the maximum dimensions for your box. All of your work and the box you create should be submitted below.
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.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
