Question

The function f(x) = 1.85x^2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.

Answer 1

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Explanation:

We can find the average rate of change of f(x) over the interval [10, 20] using the formula:

average rate of change = (f(b) - f(a))/(b - a)

where a = 10 and b = 20.

So, we have:

f(a) = f(10) = 1.85(10)^2 = 185

f(b) = f(20) = 1.85(20)^2 = 740

average rate of change = (740 - 185)/(20 - 10) ≈ 55.5

Therefore, the average rate of change of f(x) over the interval [10, 20] is approximately 55.5.