Final answer:
To find the average rate of change of a function over an interval, we need to find the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values of the endpoints.
Step-by-step explanation:
To find the average rate of change of a function over an interval, we need to find the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values of the endpoints.
In this case, the function is f(x) = 1.75x + 10x^26 and the interval is 4 < x < 12.
To find the average rate of change, we first need to calculate the function values at the endpoints:
f(4) = 1.75 * 4 + 10 * 4^26 = 7 + 10 * 4^26
f(12) = 1.75 * 12 + 10 * 12^26 = 21 + 10 * 12^26
Then we can find the difference in the function values:
f(12) - f(4) = (21 + 10 * 12^26) - (7 + 10 * 4^26)
Finally, we divide the difference in function values by the difference in x-values:
(f(12) - f(4)) / (12 - 4) = (21 + 10 * 12^26 - 7 - 10 * 4^26) / (12 - 4)
Simplifying the expression will give us the average rate of change over the interval.