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ow would you solve #57

ow would you solve #57

Calculus: Early Transcendentals
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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How would you solve #57?
1 nd to er d A(x) = 4x² + Exercise Set 3.4 56. Ideal dimensions. The amount of material used to construct a certain box is given by 6000 x² where x is the length of one side of the square base of the box, in inches, and A is the amount of material used, in square inches. a) Find the value x for which the amount of material is minimized. 315 b) What amount of material is used at the point found in part (a)? 12,000 57. Minimizing cost of materials. The cost C, in dollars, to build a fence around a rectangular field with an area of 1000 m² is given by C(x) = 8x + where x is the length of one side of the field. a) Find the value x for which the cost to build the fence is minimized. b) What is the cost at the value of x found in part (a)? Life Science 58. Blood pressure. With a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B, in millimeters of mercury (mmHg), is approximated by B(x) = 50 + 30,500x² 183,000x³, 0≤x≤ 0.16. Find the maximum blood pressure and the dosage at which it occurs.
Transcribed Image Text:1 nd to er d A(x) = 4x² + Exercise Set 3.4 56. Ideal dimensions. The amount of material used to construct a certain box is given by 6000 x² where x is the length of one side of the square base of the box, in inches, and A is the amount of material used, in square inches. a) Find the value x for which the amount of material is minimized. 315 b) What amount of material is used at the point found in part (a)? 12,000 57. Minimizing cost of materials. The cost C, in dollars, to build a fence around a rectangular field with an area of 1000 m² is given by C(x) = 8x + where x is the length of one side of the field. a) Find the value x for which the cost to build the fence is minimized. b) What is the cost at the value of x found in part (a)? Life Science 58. Blood pressure. With a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B, in millimeters of mercury (mmHg), is approximated by B(x) = 50 + 30,500x² 183,000x³, 0≤x≤ 0.16. Find the maximum blood pressure and the dosage at which it occurs.
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Calculus homework question answer, step 1, image 1

a.

to find minimum value , differentiate the function and equate to zero. 

Calculus homework question answer, step 1, image 2

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