Enrich · Mathematics Extension 1 11–12 – Year 12 · Further applications of calculus

Enrich 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

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