Chapter 2.7, Problem 12E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

(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 arguing by analogy with Exercise 11(b).

To determine

**Part (a):**

**To calculate: **The rate of change of the volume V(x) with respect to side length x that means

Explanation

**1) Concept**

Use concept of derivative to find the rate of change of the volume V(x) of a cube with respect to its edge length x

**2) Formula:**

i) The volume of a cube with edge length x is,

ii) Power Rule:

**3) Given:**

V is the volume of a cube and side length x = 3mm

**4) Calculation:**

To find

Thus, the rate of change of the volume of a cube with respect to its edge length x is,

To find

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