Expression 8: 2 minus 2 * "y" plus 2 * "x" squared * "y" minus "y" squared plus "x" * "y" squared equals "z"2−2*y+2*x2*y−y2+x*y2=z
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Since smaller loops correspond to larger z values, those loops collapse down to the location of a maximum. We'll see how to find the exact coordinates in the next folder.
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Equations for the critical points
Hide this folder from students.
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The critical points should be the solutions of the following equations. Turn them on to see where those curves intersect.
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Expression 12: "m" equals "f" left parenthesis, negative 1 , 0 , right parenthesism=f−1,0
equals=
negative 1−1
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saddle: left parenthesis, negative 1 , 0 , right parenthesis−1,0
Label:
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min: left parenthesis, 1 third , negative 1 quarter , right parenthesis13,−14
Label:
equals=
left parenthesis, 0.3 3 3 3 3 3 3 3 , negative 0.2 5 , right parenthesis0.33333333,−0.25
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saddle: left parenthesis, 1 , 0 , right parenthesis1,0
Label:
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max: left parenthesis, 1 , negative 4 , right parenthesis1,−4