Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If v is the volume of such a cube with side length x, calculate the derivative when x = 4 mm.

Question

Anton Zhang

Mathematics

13 May, 11:21

Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If v is the volume of such a cube with side length x, calculate the derivative when x = 4 mm.

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Answers (1)

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Bruce Donovan · Answer 1

48 mm ^ 2

Step-by-step explanation:

We know we have a cube of side x, therefore the volume of that cube will be equal to:

V = x ^ 3, because it is a cube and each side is the same.

Now the derivative of the volume with respect to the length (that is, x) would be:

dV / dx = 3 * (x ^ 2)

They tell us that x takes a value of 4, replacing we have:

dV / dx = 3 * (4 ^ 2) = 48

That is, 48 mm ^ 2 would be the value of dV / dx when x is equal to 4 mm.