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13 December, 11:35

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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  1. 13 December, 14:33
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    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.
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