Cuts Scrapbooking

Cuts Scrapbooking
An open box is to be done from a Scrapbook Card decoration, 40 cm by 30 cm, through the reduction of places?

An open box should be made from a decorative scrapbook card, 40 cm by 30 cm square cut corners. Find the height of the box that has the maximum volume.

Ok, I'll help with the setup here …. I assume you can do basic calculus question (derivatives and such) Ok., So that makes sense, its better if you draw a picture as is following … First, draw your rectangle of dimensions 40 x 30 labeled. Now, when we cut corners here is where it seems when bending the sides until the box. It should also be noted that every corner must be cut identical. Ok, the unknown in this problem is the "height" of the box we call the "X" Note: "x" will occur twice on each side of the current rectangle. If you were to look at the sides of your rectangle, you will notice that the dimensions can not be 40 x 30, because we cut a length of "x" out of every corner. When we rewrite the dimensions to account this, you should note that both sides are 2 (x) shorter than they were originally. This is how we relate to all our parts. When you fold the box above, shouldd recognize that its dimensions are (40-2x) X (30-2x) X "x" From here, the problem is child's play. The volume of a box is L * W * H, so its volume in terms of "x" is 1200x – 140x ^ 2 + 4x ^ 3 recall of their classes: maximum and miniums occur when the first derivative = 0. Also note, we only care about the positive values of x, and can not have negative length. 1st derivative = 1200-280x 12 x ^ 2 set equal to 0 or to find the solution graphically on a graphing calculator. My guess is that factor is not very well and you have to use the quadratic formula graphing or finding zeros. I have no right to graphic calc my hand now, but I guess you can take from here … if not, you have more important matters of this kind of questions .. Note: You can skip all phase first derivative if you understand the maximum and minimum … you can go directly to the graph of 1200x-140x ^ 2 +4 x ^ 3 notice shall have 2 separate scenarios resulting in a maximum or minimum. Good Luck and