Find and Classify Critical Points JSFH
<Text-field style="Heading 1" layout="Heading 1">Problem 5-3</Text-field> JSFH Find and classify the extreme points of the function 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
JSFH
<Text-field style="Heading 1" layout="Heading 1">Solution by Task Template</Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn Control-drag the expression for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInhGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRInlGJ0YvRjJGQUZBRkE=. Press the Enter key. JSFH Tools\342\211\273Tasks\342\211\273Browse: Calculus - Multivariate\342\211\273Optimization\342\211\273Critical Points & Second Derivative Test
Critical Points and the Second Derivative Test Objective Function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= 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 LCgqJClJJl9feF9fRzYiIiIjIiIiRigqKCIiJEYoRiVGKClJJl9feV9fR0YmRidGKEYoKiYiIiZGKClGLEYqRighIiI= List of Independent Variables 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 NyRJJl9feF9fRzYiSSZfX3lfX0dGJA== Equations 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 NyQsJiomIiIjIiIiSSZfX3hfX0c2IkYmRiYqJiIiJEYmKUkmX195X19HRihGJUYmRiYsJiooIiInRiZGJ0YmRixGJkYmKiYiIzpGJkYrRiYhIiI= Critical Points 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 NyQ3JCIiIUYkNyQjISNEIiInIyEiJiIiJA== Second Derivative Test 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 NiUvSSlMb2NhbE1pbkc2IjciL0kpTG9jYWxNYXhHRiVGJi9JJ1NhZGRsZUdGJTcjNyQjISNEIiInIyEiJiIiJA== Hessians and their Eigenvalues 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkobWFjdGlvbkdGJDYlLUkobWZlbmNlZEdGJDYoLUYjNiYtSSdtdGFibGVHRiQ2Ni1JJG10ckdGJDYnLUkkbXRkR0YkNigtSSNtbkdGJDYkUSIyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUpcm93YWxpZ25HUSFGJy8lLGNvbHVtbmFsaWduR0ZFLyUrZ3JvdXBhbGlnbkdGRS8lKHJvd3NwYW5HUSIxRicvJStjb2x1bW5zcGFuR0ZMLUY6NigtRj02JFEiMEYnRkBGQ0ZGRkhGSkZNRkNGRkZILUY3NidGT0ZPRkNGRkZILyUmYWxpZ25HUSVheGlzRicvRkRRKWJhc2VsaW5lRicvRkdRJnJpZ2h0RicvRklRJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR1EldHJ1ZUYnLyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGXm8vJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYnLyUpcm93bGluZXNHUSVub25lRicvJSxjb2x1bW5saW5lc0dGaW8vJSZmcmFtZUdGaW8vJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYnLyUqZXF1YWxyb3dzR1EmZmFsc2VGJy8lLWVxdWFsY29sdW1uc0dGY3AvJS1kaXNwbGF5c3R5bGVHRmNwLyUlc2lkZUdGZm4vJTBtaW5sYWJlbHNwYWNpbmdHRmZvLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0ZjcEZARkAvSSttc2VtYW50aWNzR0YkUSdNYXRyaXhGJy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZhcS8lK2FjdGlvbnR5cGVHUS5ydGFibGVhZGRyZXNzRicvJSlydGFibGVpZEdRKjE1MzAxOTM2OEYnLUkjbW9HRiQ2LVEiLEYnRkAvJSZmZW5jZUdGY3AvJSpzZXBhcmF0b3JHRltvLyUpc3RyZXRjaHlHRmNwLyUqc3ltbWV0cmljR0ZjcC8lKGxhcmdlb3BHRmNwLyUubW92YWJsZWxpbWl0c0dGY3AvJSdhY2NlbnRHRmNwLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRi82Ji1GIzYoRlFGYHJGPEZccUZfcUZARkBGZHFGZ3FGXHFGX3FGQA== 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
JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn
<Text-field style="Heading 1" layout="Heading 1">Solution from First Principles</Text-field>
<Text-field style="Heading 2" layout="Heading 2">Find Critical Points</Text-field> JSFH Control-drag the expression for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInhGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRInlGJ0YvRjJGQUZBRkE=. Context Menu\342\211\273Assign to a Name\342\211\273LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= JSFH JSFH Using the partial derivative operator in the Expression palette, juxtapose the two equations 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 Press the Enter key. Context Menu: Solve JSFH JSFH JSFH JSFH
JSFH
<Text-field style="Heading 2" layout="Heading 2">Second Derivative Test</Text-field> JSFH At a critical point, obtain 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 Using the partial derivative operator in the Expression palette, obtain 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. If necessary, Context Menu: Evaluate at a Point. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn Using the partial derivative operator in the Expression palette, obtain 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. If necessary, Context Menu: Evaluate at a Point. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn Using the partial derivative operator in the Expression palette, obtain 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. If necessary, Context Menu: Evaluate at a Point. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn Using equation labels, construct the test number 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= and 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 point is a minimum LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= and 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 point is a maximum 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critical point is a saddle 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 fails
JSFH
JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH JSFH