For the function find the maximum number of real zeros that the function can have, the maximum number of x-intercepts
that the function can have, and the maximum number of turning points that the graph of the function can have.
-$$f ( x ) = - x ^ { 6 } + 8 x ^ { 5 } - x ^ { 2 } - 4 x + 9$$
A) $6 ; 6 ; 5$
B) $6 ; 5 ; 5$
C) $6 ; 6 ; 6$
D) $5 ; 5 ; 6$

Question

Quizplus · Accepted Answer

The maximum number of real zeros a polynomial can have is equal to its degree, which is 6 for this polynomial. The maximum number of x-intercepts on a graph is equal to the maximum number of real zeros, so it's also 6. The maximum number of turning points for a polynomial of degree n is n-1, which is 5 for a 6th degree polynomial.

For the Function Find the Maximum Number of Real Zeros f(x)=−x6+8x5−x2−4x+9f ( x ) = - x ^ { 6 } + 8 x ^ { 5 } - x ^ { 2 } - 4 x + 9f(x)=−x6+8x5−x2−4x+9

For the Function Find the Maximum Number of Real Zeros $f ( x ) = - x ^ { 6 } + 8 x ^ { 5 } - x ^ { 2 } - 4 x + 9$