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Finding the coordinates and determining the nature of the stationary points on a polynomial function

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "extensions": [], "variables": {"y12": {"name": "y12", "group": "Ungrouped variables", "definition": "2(x12^3)-3(x12+x22)*x12^2+6*x12*x22*x12+c02", "description": "", "templateType": "anything"}, "y03": {"name": "y03", "group": "Ungrouped variables", "definition": "random(-10..10)", "description": "", "templateType": "anything"}, "y32": {"name": "y32", "group": "Ungrouped variables", "definition": "if(y12For the following function:

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\\[ \\simplify{y = 2x^3-3{(x12+x22)}x^2+6{x12*x22}x+{c02}} \\]

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Determine the coordinates and the nature of the stationary points.

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First Derivative; $y^{\\prime}(x) =$ [[4]]

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Give values of x where stationary points occur: smallest-$x_1$ =[[6]],    largest-$x_2$ = [[7]]

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Second Derivative is $~ y^{\\prime\\prime}(x) =$ [[5]]

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Values of Second derivative at stationary points: 

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$y^{\\prime\\prime}(x_1) = $[[8]]

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$y^{\\prime\\prime}(x_2) = $[[9]]

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Minimum point: $\\big($ [[0]] $ , $ [[1]] $\\big)$ and maximum point: $\\big($ [[2]] $ , $ [[3]] $\\big)$

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Enter fractions in their simplest form.

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