The optimum shape of such a box is half a cube. The corresponding cube will have a volume of 2×256 ft³ = 512 ft³ = (8 ft)³. Such a box has a square base that is 8 ft on a side. If the height is half that of the cube, it will be 4 ft.
The dimensions of your box will be 8 ft square by 4 ft high.
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If the base dimension is x ft, the area (quantity of material) is
... a = x² + 4x(256/x²)
... a = x² + 1024x⁻¹
Then the derivative of area with respect to x is
... a' = 2x -1024x⁻²
Setting this derivative to zero and solving for x gives the value of x for minimum area.
... 0 = 2x -1024/x²
... 512 = x³
... x = 8 . . . . . . . . same as above.
Graphed V hope his helped
Answer:
48 to 32 8 to 4 4 to 2 24 to 16
Step-by-step explanation:
we know that
Average Rate of Change. is the change in the y-value divided by the change in the x-value for two distinct points on the graph
So
in this problem
substitute the values in the formula above
Divide by 
both numerator and denominator
therefore
the answer is
Multiply all of those and minus and do what is said and of not serch for links ok
