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, find dVdx (in mm3/mm) when x = 5 mm. V'(5) = mm3/mm Explain the meaning of V ′(5) in the context of this problem.
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Andrew N.
(a) 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 $ dV/dx $ when $ x = 3 $ mm and explain its meaning. (b) Show that the rate of change of the volume of a cube with respect to its edge length is equal to half the surface area of the cube. Explain geometrically why this result is true by analogy with Exercise 11(b).
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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 = 5 mm. V'(5) = mm^3/mm What does V'(5) mean in this situation? V'(5) represents the rate at which the side length is increasing with respect to the volume as x reaches 5 mm. V'(5) represents the rate at which the volume is increasing as x reaches 15 mm. V'(5) represents the rate at which the volume is increasing with respect to the side length as x reaches 5 mm. V'(5) represents the volume as the side length reaches 5 mm. V'(5) represents the rate at which the volume is increasing with respect to the side length as V reaches 15 mm^3.
Adi S.
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