Part II (10%) - True or False. For each statement, select T if the statement is true, or select F if false. No justification needed. 8. (a) T F The xy-trace (on the xy-plane) of the surface x² + y² - z² = 0 is a point. (b) T F If f(0, 0) exits and g(x) = f(x,0), then fx(0,0) = gʻ(0). (c) T F If f(0, 0) = 0 and fy(0, 0) = 0, then f(x, y) has a local extreme at (0,0). (d) T F If f(0, 0) and fy(0, 0) both exists, then f(x, y) is differentiable at (0,0). (e) T F If f(x, y) is continuous on the disk D = {(x, y) | x² + y² ≤ 1}, then f(x, y) has an absolute maximum on D.
Part II (10%) - True or False. For each statement, select T if the statement is true, or select F if false. No justification needed. 8. (a) T F The xy-trace (on the xy-plane) of the surface x² + y² - z² = 0 is a point. (b) T F If f(0, 0) exits and g(x) = f(x,0), then fx(0,0) = gʻ(0). (c) T F If f(0, 0) = 0 and fy(0, 0) = 0, then f(x, y) has a local extreme at (0,0). (d) T F If f(0, 0) and fy(0, 0) both exists, then f(x, y) is differentiable at (0,0). (e) T F If f(x, y) is continuous on the disk D = {(x, y) | x² + y² ≤ 1}, then f(x, y) has an absolute maximum on D.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 17RE
Related questions
Question
![Part II (10%) - True or False. For each statement, select T if the statement is true, or select
F if false. No justification needed.
8. (a) T F The xy-trace (on the xy-plane) of the surface x² + y² - z² = 0 is a point.
(b) T F If f(0, 0) exits and g(x) = f(x,0), then fx(0,0) = gʻ(0).
(c) T F If f(0, 0) = 0 and fy(0, 0) = 0, then f(x, y) has a local extreme at (0,0).
(d) T F If f(0, 0) and fy(0, 0) both exists, then f(x, y) is differentiable at (0,0).
(e) T F If f(x, y) is continuous on the disk D = {(x, y) | x² + y² ≤ 1}, then f(x, y) has
an absolute maximum on D.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1300845a-828a-484d-8f06-319293900125%2F725a54cf-6f37-4415-93cc-f6f87f044645%2Fmnkcs6_processed.png&w=3840&q=75)
Transcribed Image Text:Part II (10%) - True or False. For each statement, select T if the statement is true, or select
F if false. No justification needed.
8. (a) T F The xy-trace (on the xy-plane) of the surface x² + y² - z² = 0 is a point.
(b) T F If f(0, 0) exits and g(x) = f(x,0), then fx(0,0) = gʻ(0).
(c) T F If f(0, 0) = 0 and fy(0, 0) = 0, then f(x, y) has a local extreme at (0,0).
(d) T F If f(0, 0) and fy(0, 0) both exists, then f(x, y) is differentiable at (0,0).
(e) T F If f(x, y) is continuous on the disk D = {(x, y) | x² + y² ≤ 1}, then f(x, y) has
an absolute maximum on D.
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