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Find the absolute maximum and minimum values of f(x, y) = x' + y? +8 on the set D where D is the closed region bounded by y = 0 and y = 5 – 5x2. Part 1: Critical Points The critical points of f are: Σ

Find the absolute maximum and minimum values of f(x, y) = x' + y? +8 on the set D where D is the closed region bounded by y = 0 and y = 5 – 5x2. Part 1: Critical Points The critical points of f are: Σ

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the absolute maximum and minimum values of f(x, y) = x + y? + 8 on the set D where D is the closed region bounded by y = 0 and y = 5 – 5x2. - Part 1: Critical Points The critical points of f are: Σ - Part 2: Boundary Work The boundary of the region can be expressed by 2 curves. Although you need to do calculations over all of the boundary pieces you will only submit your results for one of them. Along y = 5 – 5x², f can be expressed as a function of one variable g(x) = f(x, 5-5x^2 E )= x^3+(5-5x^2)^2+8 List all the points on this side of the boundary which could potentially be the absolute minimum or maximum on D. Σ - Part 3: Final Results Make sure you do the other computations along the other boundaries before you attempt this section! Find the function's absolute maximums and minimums and where they occur. The absolute maximum of f is: Σ and : occurs at Σ. The absolute minimum of f is: Σ and it occurs at
Transcribed Image Text:Find the absolute maximum and minimum values of f(x, y) = x + y? + 8 on the set D where D is the closed region bounded by y = 0 and y = 5 – 5x2. - Part 1: Critical Points The critical points of f are: Σ - Part 2: Boundary Work The boundary of the region can be expressed by 2 curves. Although you need to do calculations over all of the boundary pieces you will only submit your results for one of them. Along y = 5 – 5x², f can be expressed as a function of one variable g(x) = f(x, 5-5x^2 E )= x^3+(5-5x^2)^2+8 List all the points on this side of the boundary which could potentially be the absolute minimum or maximum on D. Σ - Part 3: Final Results Make sure you do the other computations along the other boundaries before you attempt this section! Find the function's absolute maximums and minimums and where they occur. The absolute maximum of f is: Σ and : occurs at Σ. The absolute minimum of f is: Σ and it occurs at
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