   Chapter 2.R, Problem 75E

Chapter
Section
Textbook Problem

# The mass of part of a wire is x ( 1 + x ) kilograms, where x is measured in meters from one end of the wire. Find the linear density of the wire when x = 4 m .

To determine

To find:

The linear density of the wire when x = 4 m

Explanation

1. Concept:

Use differentiation

2. Formula:

i. Product rule:

ddxfx*gx=fxddxgx+gxddx(fx)

ddxx=12x

iii. Sum rule:

ddxfx+gx=ddxfx+ddx(gx)

iv. Constant function rule:

ddxC=0

3. Given:

mx=x(1+x)

4. Calculation:

Linear density is the rate of change of mass with respect to the position at that point

Therefore,

Differentiate mass with respect to x

m'x=ddxx(1+x)

By using product rule,

m'x=x</

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