   Chapter 9.8, Problem 35E 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 (in dollars) from the sale of x units of a certain product can be described by R ( x ) =   100 x —   0.0   1 x 2 Find the instantaneous rate of change of the marginal revenue.

To determine

To calculate: The instantaneous rate of change of the marginal revenue if the revenue (in dollars) from the sale of x number of units is provided by function R(x)=100x0.01x2.

Explanation

Given Information:

The revenue (in dollars) from the sale of x number of units is provided by function R(x)=100x0.01x2.

Formula used:

Power of x rule for function f(x)=xn is f(x)=nxn1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

The instantaneous rate of change of the marginal revenue is the second derivative of the revenue function.

Calculation:

Consider the function,

R(x)=100x0.01x2

Differentiate both sides of the function with respect to x,

R(x)=ddx(100x0.01x2)=ddx(100)ddx(0

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