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Determine the global extreme values of the function on the given set without using calculus f(x, y) = 6e-(5x²+9y?), 5æ² + 9y² < 2 fmin fmax

Determine the global extreme values of the function on the given set without using calculus f(x, y) = 6e-(5x²+9y?), 5æ² + 9y² < 2 fmin fmax

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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**Objective:** Determine the global extreme values of the function on the given set without using calculus. **Function:** \[ f(x, y) = 6e^{-(5x^2 + 9y^2)} \] **Constraint/Set:** \[ 5x^2 + 9y^2 \leq 2 \] **Tasks:** - Find \( f_{\text{min}} = \) - Find \( f_{\text{max}} = \) **Notes:** - The function \( f(x, y) = 6e^{-(5x^2 + 9y^2)} \) is an exponential function with a Gaussian distribution-like shape, where the argument of the exponent, \(-(5x^2 + 9y^2)\), determines its spread and direction. - The constraint \( 5x^2 + 9y^2 \leq 2 \) describes an ellipse in the xy-plane. The task is to determine the extreme values by considering the behavior of the function under the constraint of the elliptical form without using traditional calculus methods such as differentiation.
Transcribed Image Text:**Objective:** Determine the global extreme values of the function on the given set without using calculus. **Function:** \[ f(x, y) = 6e^{-(5x^2 + 9y^2)} \] **Constraint/Set:** \[ 5x^2 + 9y^2 \leq 2 \] **Tasks:** - Find \( f_{\text{min}} = \) - Find \( f_{\text{max}} = \) **Notes:** - The function \( f(x, y) = 6e^{-(5x^2 + 9y^2)} \) is an exponential function with a Gaussian distribution-like shape, where the argument of the exponent, \(-(5x^2 + 9y^2)\), determines its spread and direction. - The constraint \( 5x^2 + 9y^2 \leq 2 \) describes an ellipse in the xy-plane. The task is to determine the extreme values by considering the behavior of the function under the constraint of the elliptical form without using traditional calculus methods such as differentiation.
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