Find the absolute maximum and minimum values of f(x, y) = y² + x² - 2x + 4 on the set D where D is the closed triangular region with vertices (4,0), (0, 3), and (0, -3). Part 1: Critical Points The critical points of fare: Part 2: Boundary Work Σ The boundary of the triangle can be expressed in 3 lines. Although you need to do calculations over all of the boundaries you will only submit your results for one of them. Find a linear equation for the side of the boundary of the region D between (4,0) and (0, 3). Σ 1or x € [0, 4] Along this side, f can be expressed as a function of one variable g(x) = f(x, Σ List all the points on this side of the boundary which could potentially be the absolute minimum or maximum on D. Σ y =

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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- 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 fis:
Σ
and it occurs at
The absolute minimum of fis:
and it occurs at
M
M
Σ
Transcribed Image Text:- 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 fis: Σ and it occurs at The absolute minimum of fis: and it occurs at M M Σ
Find the absolute maximum and minimum values of f(x, y) = y² + x² - 2x + 4 on the set D where D is the closed triangular
region with vertices (4,0), (0, 3), and (0, -3).
Part 1: Critical Points
The critical points of fare:
- Part 2: Boundary Work
The boundary of the triangle can be expressed in 3 lines. Although you need to do calculations over all of the boundaries you
will only submit your results for one of them.
Σ
y =
Find a linear equation for the side of the boundary of the region D between (4,0) and (0, 3).
Σ_1or x € [0, 4]
Along this side, f can be expressed as a function of one variable
g(x) = f(x,
Σ
List all the points on this side of the boundary which could potentially be the absolute minimum or maximum on D.
W
Transcribed Image Text:Find the absolute maximum and minimum values of f(x, y) = y² + x² - 2x + 4 on the set D where D is the closed triangular region with vertices (4,0), (0, 3), and (0, -3). Part 1: Critical Points The critical points of fare: - Part 2: Boundary Work The boundary of the triangle can be expressed in 3 lines. Although you need to do calculations over all of the boundaries you will only submit your results for one of them. Σ y = Find a linear equation for the side of the boundary of the region D between (4,0) and (0, 3). Σ_1or x € [0, 4] Along this side, f can be expressed as a function of one variable g(x) = f(x, Σ List all the points on this side of the boundary which could potentially be the absolute minimum or maximum on D. W
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