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.
