Question

# Cuboid containers $open at the top$ should be examined with regard to their volume. The figure below shows a network of such containers $x ∈ Df$. Determine a function ƒ $assignment rule and definition area D$ that describes the volume of these containers and calculate the volume of such a container if the content of the base area is 16 dm². Show that this function f has neither a local maximum nor a global maximum

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## Answer to a math question Cuboid containers $open at the top$ should be examined with regard to their volume. The figure below shows a network of such containers $x ∈ Df$. Determine a function ƒ $assignment rule and definition area D$ that describes the volume of these containers and calculate the volume of such a container if the content of the base area is 16 dm². Show that this function f has neither a local maximum nor a global maximum

Hank
4.8
A cuboid container open at the top can be considered as a box with length l, width w, and height h. The volume V of such a container can be given by the function V = lwh. If the content of the base area is given $let’s denote it by A$, and assuming the base is a square $so l = w$, we can express l and w in terms of A as l = w = sqrt$A$. The volume function then simplifies to V = Ah, where h is the height of the container. Given that A = 16 dm², the volume of the container for a specific height h would be V = 16h. The derivative of V$h$ = 16h with respect to h is dV/dh = 16, which is a constant. This means that the function V$h$ is a linear function with a constant slope, and it increases as h increases. Therefore, it doesn’t have a maximum value $neither local nor global$, as it will continue to increase as long as h increases.
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