This is a problem of maxima and minima using derivative.
In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:
V = length x width x height
That is:

We also know that the <span>bin is constructed from 48 square feet of sheet metal, s</span>o:
Surface area of the square base =

Surface area of the rectangular sides =

Therefore, the total area of the cube is:

Isolating the variable y in terms of x:

Substituting this value in V:

Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:

Solving for x:

Solving for y:

Then, <span>the dimensions of the largest volume of such a bin is:
</span>
Length = 4 ftWidth = 4 ftHeight = 2 ftAnd its volume is:
YZ = 16. The triangles are congruent. This would be AAS so YZ = 16 because of CPCTC.
Since y + x = 3, then we could say one of them equals 2 while the other is 1. y - x = 1, then we can say 3 - 1 = 2, so y would be 2 and x would be 1
Get y by itself so subtract 2x from both sides. So next it would be -4y=-2x+2. To get y by itself divide both sides by -4. So then it would be y= -2/-4x +2/-4. They both reduce down to y=1/2x-1/2. So the slope is 1/2 because the formula y=mx+b
m=slope. Hope this helps! :)
Answer:
Logarithmic
Step-by-step explanation:
For this exmaple, x is the one increasing by a third power for every y
Logarithmic is the opposite of exponential
Exponential is when y is the one increasing by a power for every x.
Therefore this one is logarithmic.