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4.7.5. Find the local extrema of the function f(x, y) = x² +xy– 4x+y² – 7y R?. on

4.7.5. Find the local extrema of the function f(x, y) = x² +xy– 4x+y² – 7y R?. on

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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Prove Problem 4.7.5

**4.7.3** Explain, making whatever reasonable assumptions seem to be helpful, why the _n_-dimensional conceptual analogue of Figure 4.9 should have \(3^n\) pictures. How does this relate to Figure 4.8? **4.7.4** Find the extreme values taken by \(f(x, y) = xy(4x^2 + y^2 - 16)\) on the quarter-ellipse \[ E = \{(x, y) \in \mathbb{R}^2 : x \geq 0, y \geq 0, 4x^2 + y^2 \leq 16\}. \] **4.7.5** Find the local extrema of the function \(f(x, y) = x^2 + xy - 4x + \frac{3}{2}y^2 - 7y\) on \(\mathbb{R}^2\).
Transcribed Image Text:**4.7.3** Explain, making whatever reasonable assumptions seem to be helpful, why the _n_-dimensional conceptual analogue of Figure 4.9 should have \(3^n\) pictures. How does this relate to Figure 4.8? **4.7.4** Find the extreme values taken by \(f(x, y) = xy(4x^2 + y^2 - 16)\) on the quarter-ellipse \[ E = \{(x, y) \in \mathbb{R}^2 : x \geq 0, y \geq 0, 4x^2 + y^2 \leq 16\}. \] **4.7.5** Find the local extrema of the function \(f(x, y) = x^2 + xy - 4x + \frac{3}{2}y^2 - 7y\) on \(\mathbb{R}^2\).
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