For a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B is approximated by the function below. Find the maximum blood pressure and the dosage at which it occurs. B(x)=390x²-1560x³, 0≤x≤0.25 The maximum is obtained for a dosage of (Round to two decimal places as needed.) NE
For a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B is approximated by the function below. Find the maximum blood pressure and the dosage at which it occurs. B(x)=390x²-1560x³, 0≤x≤0.25 The maximum is obtained for a dosage of (Round to two decimal places as needed.) NE
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![**Understanding Drug Dosage and Blood Pressure**
For a dosage of \( x \) cubic centimeters (cc) of a certain drug, the resulting blood pressure \( B \) is approximated by the function below. Find the maximum blood pressure and the dosage at which it occurs.
\[ B(x) = 390x^2 - 1560x^3, \quad 0 \le x \le 0.25 \]
---
The maximum is obtained for a dosage of [ ].
*(Round to two decimal places as needed.)*
---
### Explanation:
This function represents the relationship between the dosage of a drug and its effect on blood pressure. The goal is to determine the dosage \( x \) that results in the maximum blood pressure.
The mathematical model is a cubic function with constraints on \( x \) between 0 and 0.25. By analyzing this function, you can identify the peak, where the blood pressure is at its highest before it begins to decrease again as the dosage increases.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2ceb2d65-29b4-49d4-9830-4ba06589987b%2F1462f562-ccfa-4051-add2-ce9b8123a11f%2Fpjmb4fp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Drug Dosage and Blood Pressure**
For a dosage of \( x \) cubic centimeters (cc) of a certain drug, the resulting blood pressure \( B \) is approximated by the function below. Find the maximum blood pressure and the dosage at which it occurs.
\[ B(x) = 390x^2 - 1560x^3, \quad 0 \le x \le 0.25 \]
---
The maximum is obtained for a dosage of [ ].
*(Round to two decimal places as needed.)*
---
### Explanation:
This function represents the relationship between the dosage of a drug and its effect on blood pressure. The goal is to determine the dosage \( x \) that results in the maximum blood pressure.
The mathematical model is a cubic function with constraints on \( x \) between 0 and 0.25. By analyzing this function, you can identify the peak, where the blood pressure is at its highest before it begins to decrease again as the dosage increases.
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