   Chapter 9.5, Problem 45E ### 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

# Response to a drug The reaction R to an injection of a drug is related to the dosage x (in milligrams) according to R ( x ) = x 2 ( 500 − x 3 ) where 1000 mg is the maximum dosage. If the rate of reaction with respect to the dosage defines the sensitivity to the drug, find the sensitivity.

To determine

To calculate: The rate of reaction with respect to the dosage defines the sensitivity to the drug if the reaction R to an injection of a drug is related to the dosage x (in milligrams) is given by the equation R(x)=(x2).(500x3).

Explanation

Given Information:

The reaction R to an injection of a drug is related to the dosage x (in milligrams) is given by the equation R(x)=(x2).(500x3).

Formula Used:

If two functions are given in the form f(x)+g(x), then the derivative is given as:

ddx(f+g)=dfdx+dgdx

The rate of the function is the first derivative of the function.

Power rule of the derivative is xn=nxn1.

Calculation:

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

Multiply the factors and rewrite the above equation as,

R(x)=(x2)

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