Final answer:
The average rate of change of the function f(x) = 3 - 4x from x = 1 to x = 6 is -4.
Step-by-step explanation:
The average rate of change of a function over an interval is found by taking the difference in function values at the endpoints of the interval and dividing by the length of the interval.
We have the function f(x) = 3 - 4x, and we want to find the average rate of change from x = 1 to x = 6. First, we calculate the function values at x = 1 and x = 6:
- f(1) = 3 - 4(1) = -1
- f(6) = 3 - 4(6) = -21
Next, we use the formula:
average rate of change = (f(6) - f(1)) / (6 - 1)
Substituting the calculated values:
average rate of change = (-21 - (-1)) / (6 - 1) = -20 / 5 = -4
Therefore, the average rate of change of the function from x = 1 to x = 6 is -4.