5. [Local Optimization] Let f = f(x,y) — x³ + x²y — y² — 4y. (a) Find and classify all critical points of f on all of R². (b) Find and classify all critical points of f on the line y - z. (c) Find and classify all critical points of f on the curve y = 2². -
5. [Local Optimization] Let f = f(x,y) — x³ + x²y — y² — 4y. (a) Find and classify all critical points of f on all of R². (b) Find and classify all critical points of f on the line y - z. (c) Find and classify all critical points of f on the curve y = 2². -
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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![5. **[Local Optimization]** Let \( f = f(x, y) = x^3 + x^2y - y^2 - 4y \).
(a) Find and classify all critical points of \( f \) on all of \( \mathbb{R}^2 \).
(b) Find and classify all critical points of \( f \) on the line \( y = x \).
(c) Find and classify all critical points of \( f \) on the curve \( y = x^2 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34e6895f-8abd-4c7c-a38e-4b1b563dc71a%2Fe5ef0230-37cc-464f-a7db-e5a4a6212af5%2Fdoihike_processed.png&w=3840&q=75)
Transcribed Image Text:5. **[Local Optimization]** Let \( f = f(x, y) = x^3 + x^2y - y^2 - 4y \).
(a) Find and classify all critical points of \( f \) on all of \( \mathbb{R}^2 \).
(b) Find and classify all critical points of \( f \) on the line \( y = x \).
(c) Find and classify all critical points of \( f \) on the curve \( y = x^2 \).
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