Problem 5. Let f(x,y)=x²2w | y² 2y. (a) Find the local minima, local maxima, and the saddle points of f. (b) Sketch the region A = {(x, y) a>0, y>0, y <3 z). (c) Find the absolute maximum and the absolute minimum of f on A.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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**Problem 5.** Let \( f(x, y) = x^2 - 2x + y^2 - 2y \).

(a) Find the local minima, local maxima, and the saddle points of \( f \).

(b) Sketch the region \( A = \{(x, y) \,|\, x \geq 0, \, y \geq 0, \, y \leq 3 - x\} \).

(c) Find the absolute maximum and the absolute minimum of \( f \) on \( A \).
Transcribed Image Text:**Problem 5.** Let \( f(x, y) = x^2 - 2x + y^2 - 2y \). (a) Find the local minima, local maxima, and the saddle points of \( f \). (b) Sketch the region \( A = \{(x, y) \,|\, x \geq 0, \, y \geq 0, \, y \leq 3 - x\} \). (c) Find the absolute maximum and the absolute minimum of \( f \) on \( A \).
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