   Chapter 11.1, Problem 46E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Supply Suppose that the supply of x units of a product at price p dollars per unit is given by p =   10   +   50   ln   ( 3 x   +   1 ) (a) Find the rate of change of supply price with respect to the number of units supplied.(b) Find the rate of change of supply price when the number of units is 33.(c) Approximate the price increase associated with the number of units supplied changing from 33 to 34.

(a)

To determine

To calculate: The rate of change of supply price with respect to the number of units supplied.

Explanation

Given Information:

The prize p of x units of a product is given by,

p=10+50ln(3x+1)

Formula Used:

According to the property of derivative,

ddx(lnx)=1x

Chain rule,

ddxf(g(x))=fg(x)g(x)

Calculation:

Consider the provided function p=10+50ln(3x+1).

The rate of change of supply price with respect to the number of units supplied is given by,

dpdx=ddx(10+50ln(3x+1))=ddx(l0)+ddx(50ln(3x+1))=ddx(l0)+50ddx(ln(3x+1))

Use the chain rule to get,

dpd

(b)

To determine

To calculate: The rate of change of supply price if the number of units is 33.

(c)

To determine

To calculate: The price increase associated with the number of units supplied changing from 33 to 34.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### sinx=ex+ex2

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### The area of the shaded region is given by:

Study Guide for Stewart's Multivariable Calculus, 8th

#### Simplify each expression. logbb4

College Algebra (MindTap Course List) 