(a) Explanation Given information: Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. Calculation: If V is the volume of a cubic sodium chlorate crystal with side lengthx , then V ( x ) = x 3 Where x is measured in mm Using the Power Rule, the rate of change of volume with respect to the side length x is given by the derivative: d V d x = 3 x 2 So that, at x = 3 mm, we have < (b) To determine To show: 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.

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Question

Chapter 3.3, Problem 54E

(a)

To determine

To calculate: dV/dx when x = 3 mm and explain its meaning.

(b)

To determine

To show: 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.

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Chapter 3.3, Problem 53E

Chapter 3.3, Problem 55E

Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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d V / d x when x = 3 mm and explain its meaning.

Solution Summary: The author calculates the rate of change of the volume of a cube with respect to its edge length by using the Power Rule.