Describe how to determine the average rate of change between x=4 and x=6 for the function f(x)=2x^3+4. Include the average rate of change in your answer.

Step-by-step explanation:

Average rate of change is the same thing as the slope of the line between 2 points. What we have are the x values of each of 2 coordinates. What we don't have are the y values that go with those. But we can find them! Aren't you so happy?

We can find the y value that corresponds to each of those x values by evaluating the function at each x value, one at a time. That means plug in 4 for x and solve for y, and plug in 6 for x and solve for y.

and doing the math on that gives us

f(4) = 132 and the coordinate is (4, 132).

Doing the same for 6:

and doing the math on that gives us

f(6) = 436 and the coordinate is (6, 436). Now we can use the slope formula to find the average rate of change (aka slope):

where m represents the slope

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3