The table shows the values of a function f(x). what is the average rate of change of f(x) from 1 to 4?

x f(x)
0 500
1 484
2 436
3 356
4 244
5 100

-80

Step-by-step explanation:

The average rate of change is

a.r.c = f(4) - f(1)

             4-1

f(4) = 244 and f(1) = 484

a.r.c = 244  - 484

             3

        = -240/3

      =-80

The average rate of change of f(x) from 1 to 4 is -80.

Step-by-step explanation:

The average rate of change of f(x) from a to b is defined as

The average rate of change of f(x) from 1 to 4 is defined as

From the given table it is clear that the the value of the function is 244 at x=4 and 484 at x=1. So f(4)=244 and f(1)=484. Put these values in the above equation.

Therefore the average rate of change of f(x) from 1 to 4 is -80.

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."