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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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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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.
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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