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Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus · Multiplicity of zeroes of polynomial functions · Topic: Calculus · Year 11, 12

Prove that if α is a zero of multiplicity m, meeting the x -axis at A(α,0), then if m = 1, the curve crosses the x -axis at A at an acute or obtuse angle; if m > 1 is even, the curve is tangent to the x -axis at A and does not cross it; if m > 1 is odd, the curve has a horizontal inflection at A

Dot point ID extension-1-year-12-further-applications-of-calculus/dp-c420ec27 · See it on the NSW Curriculum website ↗

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Outcomes for this focus area (ME1-12-05)

ME1-12-05 applies calculus to solve problems involving polynomials, further rates of change, areas and volumes and differential equations

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