The reaction of the body to a dose of medicine can sometimes be represented by an equation of the form R = M² where C is a positive constant and M is the amount of medicine absorbed in the blood. If the reaction is a change in blood pressure, R is measured in millimeters of mercury. If the reaction is a change in temperature, R is measured in degrees, dR and so on. Find dM This derivative, as a function of M, is called the sensitivity of the body to the medicine. dR dM ***
The reaction of the body to a dose of medicine can sometimes be represented by an equation of the form R = M² where C is a positive constant and M is the amount of medicine absorbed in the blood. If the reaction is a change in blood pressure, R is measured in millimeters of mercury. If the reaction is a change in temperature, R is measured in degrees, dR and so on. Find dM This derivative, as a function of M, is called the sensitivity of the body to the medicine. dR dM ***
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Title: Understanding the Sensitivity of the Body to Medication**
The reaction of the body to a dose of medicine can sometimes be represented by an equation of the form:
\[ R = M^2 \left( \frac{C}{2} - \frac{M}{3} \right) \]
where \( C \) is a positive constant and \( M \) is the amount of medicine absorbed in the blood.
**Contextual Understanding:**
- **Reaction Measures:**
- If the reaction is a change in blood pressure, \( R \) is measured in millimeters of mercury.
- If the reaction is a change in temperature, \( R \) is measured in degrees.
**Task:**
We are tasked with finding \(\frac{dR}{dM}\), the derivative of \( R \) with respect to \( M \). This derivative, as a function of \( M \), is called the sensitivity of the body to the medicine.
**Graph/Diagram Explanation:**
There are no explicit graphs or diagrams provided in the image, but the equation and derivative are visually represented in a rectangular input field where users can calculate \(\frac{dR}{dM}\).
**Actionable Steps:**
1. **Differentiate** the equation \( R = M^2 \left( \frac{C}{2} - \frac{M}{3} \right) \) with respect to \( M \).
2. **Analyze** the resulting function to understand sensitivity at different levels of medicine \( M \).
Tools such as symbolic computation tools or manual calculus can be used to derive the result.
End of transcription.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10b1f275-2c41-4985-b23a-aa3382c0d493%2Fa540105f-c27b-4b1d-b60b-48fcef853ff7%2Fkcspw6k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding the Sensitivity of the Body to Medication**
The reaction of the body to a dose of medicine can sometimes be represented by an equation of the form:
\[ R = M^2 \left( \frac{C}{2} - \frac{M}{3} \right) \]
where \( C \) is a positive constant and \( M \) is the amount of medicine absorbed in the blood.
**Contextual Understanding:**
- **Reaction Measures:**
- If the reaction is a change in blood pressure, \( R \) is measured in millimeters of mercury.
- If the reaction is a change in temperature, \( R \) is measured in degrees.
**Task:**
We are tasked with finding \(\frac{dR}{dM}\), the derivative of \( R \) with respect to \( M \). This derivative, as a function of \( M \), is called the sensitivity of the body to the medicine.
**Graph/Diagram Explanation:**
There are no explicit graphs or diagrams provided in the image, but the equation and derivative are visually represented in a rectangular input field where users can calculate \(\frac{dR}{dM}\).
**Actionable Steps:**
1. **Differentiate** the equation \( R = M^2 \left( \frac{C}{2} - \frac{M}{3} \right) \) with respect to \( M \).
2. **Analyze** the resulting function to understand sensitivity at different levels of medicine \( M \).
Tools such as symbolic computation tools or manual calculus can be used to derive the result.
End of transcription.
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