For the function f(x) = 5x, determine the average rate of change of f(x) with respect to x over the interval -6<x<2.
1. 5
2. 12
3.-5
4. 5/4
(f(2)-f(-6))/(2-(-6))
To determine the average rate of change of a function over a given interval, we need to find the difference in the function's values at the endpoints of the interval and divide it by the difference in the input values.
In this case, we are given the function f(x) = 5x and the interval -6 < x < 2. To find the average rate of change, we need to calculate f(2) and f(-6), and find the difference in their values.
First, let's find f(2):
f(2) = 5 * 2 = 10
Now, let's find f(-6):
f(-6) = 5 * (-6) = -30
Now we can find the difference in their values:
10 - (-30) = 10 + 30 = 40
Next, we need to find the difference in the input values:
2 - (-6) = 2 + 6 = 8
Finally, we divide the difference in the function's values by the difference in the input values:
40 / 8 = 5
Therefore, the average rate of change of f(x) with respect to x over the interval -6 < x < 2 is 5.
So the correct answer is 1. 5.