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Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y=75 and P = x²y is maximized a. Solve x + y = 75 for y. y= b. Substitute the result from part a into the equation P = x²y for the variable that is to be maximized. c. Find the domain of the function P found in part b. (Simplify your answer. Type your answer in interval notation.) d. Find Solve the equation dP dx dP X dx Solve the equation. =(Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). dP dx P(0) = (Simplify your answer.) Determine P(50) 66°F Mostly cloudy = 0. C...

Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y=75 and P = x²y is maximized a. Solve x + y = 75 for y. y= b. Substitute the result from part a into the equation P = x²y for the variable that is to be maximized. c. Find the domain of the function P found in part b. (Simplify your answer. Type your answer in interval notation.) d. Find Solve the equation dP dx dP X dx Solve the equation. =(Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). dP dx P(0) = (Simplify your answer.) Determine P(50) 66°F Mostly cloudy = 0. C...

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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Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y=75 and P = x²y is maximized a. Solve x + y = 75 for y. y= b. Substitute the result from part a into the equation P = x²y for the variable that is to be maximized. c. Find the domain of the function P found in part b. (Simplify your answer. Type your answer in interval notation.) dP d. Find Solve the equation X dx dP dx Solve the equation. =(Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). dP dx P(0) = (Simplify your answer.) Determine P(50) 66°F Mostly cloudy = 0.
Transcribed Image Text:Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y=75 and P = x²y is maximized a. Solve x + y = 75 for y. y= b. Substitute the result from part a into the equation P = x²y for the variable that is to be maximized. c. Find the domain of the function P found in part b. (Simplify your answer. Type your answer in interval notation.) dP d. Find Solve the equation X dx dP dx Solve the equation. =(Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). dP dx P(0) = (Simplify your answer.) Determine P(50) 66°F Mostly cloudy = 0.
Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y=75 and P = x²y is maximized UA dP dx Solve the equation. X= (Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). UA P(0) = (Simplify your answer.) Determine P(50). P(50) = (Simplify your answer.) Find P(75). P(75)= (Simplify your answer.) f. Give the maximum value of P, as well as the two numbers x and y for which x2y is that value. The maximum value of P is The values of x and y are x = 66°F Mostly cloudy =and y = Q C...
Transcribed Image Text:Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value of P. x+y=75 and P = x²y is maximized UA dP dx Solve the equation. X= (Use a comma to separate answers as needed.) e. Evaluate P at any solutions found in part d, as well as the endpoints of the domain found in part c. Find P(0). UA P(0) = (Simplify your answer.) Determine P(50). P(50) = (Simplify your answer.) Find P(75). P(75)= (Simplify your answer.) f. Give the maximum value of P, as well as the two numbers x and y for which x2y is that value. The maximum value of P is The values of x and y are x = 66°F Mostly cloudy =and y = Q C...
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