Final answer:
To find the average rate of change of the area of a circle on the interval [4, 4.01], we can use the formula A(r) = πr^2.
Step-by-step explanation:
To find the average rate of change of the area of a circle on the interval [4, 4.01], we can use the formula A(r) = πr^2. Substituting the values, we have A(4) = π(4^2) = 16π, and A(4.01) = π(4.01^2) = 16.0801π.
The average rate of change is then calculated by finding the difference in the area values and dividing by the difference in the radius values:
average rate of change = (A(4.01) - A(4)) / (4.01 - 4) = (16.0801π - 16π) / 0.01 ≈ 0.0801π / 0.01 ≈ 8.01π.