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Consider a polynomial p (x) with a degree of 9. What is the largest possible number of x-intercepts and the largest possible number of relative max/min?

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  1. Today, 13:42
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    The largest possible number of x intercept is 9 while the largest possible number of relative max/min is 8

    Step-by-step explanation:

    For any polynomial of degree n with distinct and real solutions, it can have at most n different x intercepts. This would imply it can have at most 9 distinct real solutions.

    It can also have at most n-1 relative max/min in alternating order. This is best illustrated when such polynomial is sketched on a graph.

    For example a quadratic expression is a polynomial of degree 2 and has at most 2 distinct solutions and 1 relative max/min.

    In this question, for the polynomial, its degree (n) = 9

    So it can have at most 9 x intercepts and at most 8 relative max/min.
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