How do you find the average rate of change for the function f(x) =x^3 on the indicated intervals [2,h]?
1 Answer
Oct 10, 2015
Explanation:
The average rate of change is slope, which can be formulated by:
(y_1 - y_2)/(x_1 - x_2)
We have both x values, 2 and h, and therefore we can get the y values by plugging the x values back into the function:
f(2) = 2^3 = 8
f(h) = h^3
Now we can plug everything into the original equation:
(8-h^3)/(2-h)
We can take out a negative to make it look like this:
(h^3 - 8)/(h-2)
The top in this case is a difference of cubes, and can be simplified to this:
((h-2)(h^2 + 2h + 4))/(h-2)
We can then cancel the(h-2) value on the top and bottom.
(cancel(h-2)(h^2 + 2h + 4))/(cancel(h-2)
This leaves us with our answer
Hope this helped!