Question: Need help with part (b) 236 CHAPTER 3 Differentiation Rules 14. (a) Sodium chlorate crystals are easy to grow in the shape of cubes by

Need help with part (b)

236 CHAPTER 3 Differentiation Rules 14. (a) Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlo- rate 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 arguing by analogy with Exercise 13(b)

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