   Chapter 10, Problem 45RE ### 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

# Reaction to a drug The reaction R to an injection of a drug is related to the dose x (in milligrams) according to R ( x ) = x 2 ( 500 − x 3 ) Find the dose that yields the maximum reaction.

To determine

To calculate: The dose that yields the maximum reaction if the reaction R to an injection of a drug related to the dose x(in milligrams) according to R(x)=x2(500x3).

Explanation

Given Information:

The provided equation is R(x)=x2(500x3), where dose is in x(in milligrams).

Formula Used:

The total profit function is:

P(x)=R(x)C(x)

Where R(x)andC(x) are total revenue function and total cost function.

Calculation:

Consider the provided equation R(x)=x2(500x3),

Simplify the equation further:

R(x)=x2(500x3)=500x2x33

In order to maximize the dose, the following steps have to followed:

Take out the first derivative of the equation by the power rule,

R=ddx(500x2x33)=500ddx(x2)ddx(x33)=1000xx2

Put the value of R=0,

1000xx2=0x(1000x)=0

Thus,

x=0

And,

x=1000

The quantity cannot be negative

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