What is the average rate of change of the function over the interval x = 0 to x = 8? f(x)=2x−1/3x+5 enter your answer, as a fraction, in the box.

15 2/3, or 47/3

Step-by-step explanation:

I'm going to assume, correctly or not, that you actually meant f(x) = 2x^2 - (1/3)x + 5.  Double check on this right now, please.

If I'm right, then evaluate f(x) at x = 0 and x = 8:

f(0) = 5

and

f(8) = 2(8)^2 - (1/3)(8) + 5 = 128 - 8/3 + 5 = 133  - (2 2/3), or:   130 1/3

Then the average rate of change of f(x) = 2x^2 - (1/3)x + 5 over the interval [0,8] is:

                130 1/3 - 5         125 1/3

a. r. c. = = = 15 2/3, or 47/3

                     8 - 0                  8

step-by-step explanation:

here's what happens:

1) the graph of f   = x^2 is shifted 2 units to the right.

2) the resulting graph is reflected in the x-axis, so that the parabola now opens down.

3) this final result is transformed up by 5 units.