What is the maximum number of turns in the graph of this function? f(x)=x^4-x^3 3x 1

Maximum number of turns: 3

Step-by-step explanation:

1. By definition, a polynomial of degree, has a maximum turning points of .

2. Therefore, if you have the polynomial given in the problem, which is a polynomial of degree 4. The maximum number of turns can be obtained as following:

3. Therefore, you can conclude that the maximum number of turns are 3.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."