Show that the function f(x,y)=8x^2 y subject to 3x−y=9 does not have an absolute minimum or maximum. (Hint: Solve the constraint for y and substitute into f.) Solve the constraint for y. y = ? Substitute into f. f(x,y)= ? Determine the behavior of f as x approaches −∞. limx→−∞f(x,y)= ? Determine the behavior of f as x approaches ∞. limx→∞f(x,y)= ? Does this show that f does not have an absolute maximum or minimum? 1. No
Show that the function f(x,y)=8x^2 y subject to 3x−y=9 does not have an absolute minimum or maximum. (Hint: Solve the constraint for y and substitute into f.) Solve the constraint for y. y = ? Substitute into f. f(x,y)= ? Determine the behavior of f as x approaches −∞. limx→−∞f(x,y)= ? Determine the behavior of f as x approaches ∞. limx→∞f(x,y)= ? Does this show that f does not have an absolute maximum or minimum? 1. No
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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Question
Show that the function f(x,y)=8x^2 y subject to 3x−y=9 does not have an absolute minimum or maximum. (Hint: Solve the constraint for y and substitute into f.)
Solve the constraint for y.
y = ?
Substitute into f.
f(x,y)= ?
Determine the behavior of f as x approaches
−∞.
limx→−∞f(x,y)= ?
Determine the behavior of f as x approaches
∞.
limx→∞f(x,y)= ?
Does this show that f does not have an absolute maximum or minimum?
1. No
2. Yes
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