Explanation Given Information: The volume of cube is increasing it at a rate of 64 in 2 / sec and length of each edge is 6 in . Formula used: The volume of a cube of edge x is given by: V = x 3 According to the chain rule, if f and g are differentiable functions with y = f ( u ) and u = g ( x ) , then y is a differentiable function of x and: d y d x = d y d u ⋅ d u d x Calculation: Consider the volume of a cube of edge x is: V = x 3 Now, differentiate both sides with respect to t to get: d d t ( V ) = d d t ( x 3 ) Now, use the chain rule: d y d x = d y d u ⋅ d u d x To obtain the derivative of x 3 as:

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Author: HARSHBARGER

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Chapter 11.4, Problem 15E

To determine

To calculate: The rate of change of length of each edge if the volume of cube is increasing it at a rate of 64in2/sec and length of each edge is 6in.

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Chapter 11.4, Problem 14E

Chapter 11.4, Problem 16E

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Chapter 11 Solutions

MATHEMATICAL APPL F/MGMT LIFE (LL) FDS

Ch. 11.1 - 1. Ch. 11.1 - 2. If Ch. 11.1 - Prob. 3CP Ch. 11.1 - 4. Find . Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Find the derivatives of the functions in Problems...

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The rate of change of length of each edge if the volume of cube is increasing it at a rate of 64 in 2 / sec and length of each edge is 6 in .

Solution Summary: The author explains how to calculate the rate of change of length of each edge if the volume of cube is increasing it.

To calculate: The rate of change of length of each edge if the volume of cube is increasing it at a rate of 64in2/sec and length of each edge is 6in.

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Chapter 11 Solutions