   Chapter 9.6, Problem 38E Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

Revenue The revenue from the sale of x units of a product is R =   15 ( 3 x   +  1 ) − 1 +  50 x  –  15    Find the marginal revenue when 40 units are sold. Interpret your result.

To determine

To calculate: The marginal revenue when 40 units are sold if the revenue from the sale of a product is R=15(3x+1)1+50x15 where x is the number of units sold. There are 40 units sold.

Explanation

Given Information:

The revenue from the sale of a product is R=15(3x+1)1+50x15 where x is the number of units sold. There are 40 units sold.

Formula used:

According to the power rule, if f(x)=xn, then,

f(x)=nxn1

According to the property of differentiation, if a function is of the form, g(x)=cf(x), then,

g(x)=cf(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

According to the product rule, if f(x)=u(x)v(x), then

f(x)=u(x)v(x)+v(x)u(x)

According to the property of differentiation, if a function is of the form y=un, where u=g(x),

dydx=nun1dudx

Calculation:

Consider the provided function,

R=15(3x+1)1+50x15

Consider (3x+1) to be u,

R=15u1+50x15

Differentiate both sides with respect to x,

dRdx=ddx(15u1+50x15)=ddx(15u1)+ddx(50x)ddx(15)=15ddx(u1)+50ddx(x)ddx(15)

Simplify using the power rule and rule for constants,

dRdx=15(

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