Chapter 2.7, Problem 17E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

The mass of the part of a metal rod that lies between its left end and a point *x* meters to the right is
*x* is (a) 1 m, (b) 2 m, and

(c) 3 m. Where is the density the highest? The lowest?

To determine

**To find:** The linear density when x is:

(a) 1m(b) 2m, and(c) 3m then decide where is the density highest & lowest?

Explanation

**1) Concept:**

The linear density of the rod is the derivative of mass (m) with respect to length (x).

**2) Formula:**

i. The linear density

ii. Power rule of derivative:

**3) Given:**

(a) x = 1m (b) x = 2m, and (c) x = 3m

Mass = m = 3x^{2} as shown in figure.^{ }

**4) Calculation:**

By using above formula, linear density

Substitute m = 3x^{2} and find derivative with respect to x.

Linear density

By using power rule of derivative,

Linear density

**(a)**To find linear density at x = 1, substitute x = 1 in linear density ρ =

Linear density

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