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f(x,y) = x³y² The critical point at the origin is: ? ? f(x,y)=1-z²y² a local maximum a local minimum The critical point at the origin is: neither a local maximum nor a local minimum f(x,y)=zy²

f(x,y) = x³y² The critical point at the origin is: ? ? f(x,y)=1-z²y² a local maximum a local minimum The critical point at the origin is: neither a local maximum nor a local minimum f(x,y)=zy²

Advanced Engineering Mathematics
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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(1 point) The discriminant fer fy-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 a=f(x, y) looks like. Be sure that you can explain your reasoning! f(x,y) = x³y² The critical point at the origin is: ? ? f(x,y)=1-2²y² a local maximum a local minimum The critical point at the origin is: neither a local maximum nor a local minimum f(x,y)= The critical point at the origin is: ? f(x,y)=z³y² The critical point at the origin is: ? 1(2,3)=z³y² The critical point at the origin is: ? f(x,y)=z³y² The critical point at the origin is: ?
Transcribed Image Text:(1 point) The discriminant fer fy-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 a=f(x, y) looks like. Be sure that you can explain your reasoning! f(x,y) = x³y² The critical point at the origin is: ? ? f(x,y)=1-2²y² a local maximum a local minimum The critical point at the origin is: neither a local maximum nor a local minimum f(x,y)= The critical point at the origin is: ? f(x,y)=z³y² The critical point at the origin is: ? 1(2,3)=z³y² The critical point at the origin is: ? f(x,y)=z³y² The critical point at the origin is: ?
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