Consider the function f(x, y) = x²y + y3³ - 48y. f has a maximum f has a minimum く at (-4√3,0). at (0, 4). f has some other critical point at (0, 0). f has some other critical point at (4√3,0). f has a maximum at (0,-4).
Consider the function f(x, y) = x²y + y3³ - 48y. f has a maximum f has a minimum く at (-4√3,0). at (0, 4). f has some other critical point at (0, 0). f has some other critical point at (4√3,0). f has a maximum at (0,-4).
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 3SE: How are the absolute maximum and minimum similar to and different from the local extrema?
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Transcribed Image Text:Consider the function f(x, y) = x²y+y³ - 48y.
f has
a maximum
at (-4√3,0)
at (0, 4).
f has a minimum
f has
some other critical point at (0,0).
f has
some other critical point at
at (4√3,0).
f has
a maximum
at (0,-4).
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Step 1: First partial derivatives
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VIEWStep 3: Discriminant function
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VIEWStep 5: Classification of the second critical point
VIEWStep 6: Classification of the third critical point
VIEWStep 7: Classification of the fourth critical point
VIEWStep 8: Classification of the fifth critical point
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