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Answer :
Answer:
Absolutely, the average rate of change of a function represents the slope of the secant line that intersects the graph of the function at the interval's endpoints. Let's find the average rate of change for f(x) = 7x - 6 over the interval [2, 6].
Formula for Average Rate of Change:
The average rate of change of a function f(x) over the interval [a, b] is calculated as:
Average Rate of Change = (f(b) - f(a)) / (b - a)
Applying the formula:
Identify the function: f(x) = 7x - 6
Identify the interval: [a, b] = [2, 6]
Find f(b) and f(a):
f(b) = f(6) = (7 * 6) - 6 = 42 - 6 = 36
f(a) = f(2) = (7 * 2) - 6 = 14 - 6 = 8
Calculate the average rate of change:
Average Rate of Change = (f(b) - f(a)) / (b - a)
= (36 - 8) / (6 - 2)
= 28 / 4
= 7
Answer:
The average rate of change of f(x) = 7x - 6 over the interval [2, 6] is 7. This means the secant line intersecting the graph of the function at x = 2 and x = 6 has a slope of 7.
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