Section 14.7: Problem 8 Previous Problem Problem List Next Problem ( , The discriminant fxx fyy-fy is zero at the origin for each of the following functions, so the Second Derivative Test fails there. Determine whether the function has a maximum, a minimum, or neither at the origin by imagining what the surface z = f(x, y) looks like. Be sure that you can explain your reasoning! f(x, y) = x¹y4 The critical point at the origin is f(x, y) = 1- x4y4 The critical point at the origin is ? a local maximum a local minimum neither a local maximum nor a local minimum f(x, y) = xy4 The critical point at the origin is: ? f(x, y) = x³y4 The critical point at the origin is: ? f(x, y) = x³y³ The critical point at the origin is: ? f(x, y) = x²6 The critical point at the origin is: ? + # + +
Section 14.7: Problem 8 Previous Problem Problem List Next Problem ( , The discriminant fxx fyy-fy is zero at the origin for each of the following functions, so the Second Derivative Test fails there. Determine whether the function has a maximum, a minimum, or neither at the origin by imagining what the surface z = f(x, y) looks like. Be sure that you can explain your reasoning! f(x, y) = x¹y4 The critical point at the origin is f(x, y) = 1- x4y4 The critical point at the origin is ? a local maximum a local minimum neither a local maximum nor a local minimum f(x, y) = xy4 The critical point at the origin is: ? f(x, y) = x³y4 The critical point at the origin is: ? f(x, y) = x³y³ The critical point at the origin is: ? f(x, y) = x²6 The critical point at the origin is: ? + # + +
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Section 14.7: Problem 8
Previous Problem Problem List Next Problem
(
The discriminant fxx fyy-fy is zero at the origin for each of the following functions, so the Second Derivative Test fails there. Determine whether the function has a
maximum, a minimum, or neither at the origin by imagining what the surface z = f(x, y) looks like. Be sure that you can explain your reasoning!
f(x, y) = x¹y4
The critical point at the origin is ✓ ?
f(x, y) = 1 - x¹y4
The critical point at the origin is
a local maximum
a local minimum.
neither a local maximum nor a local minimum
f(x, y) = xy4
The critical point at the origin is: ?
f(x, y) = x³y4
The critical point at the origin is: ?
f(x, y) = x³y³
The critical point at the origin is: ?
f(x, y) = x²y6
The critical point at the origin is: ?
#
+
+
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