To calculate the average rate of change of a function over an interval, you need to find the difference in the function values at the endpoints of the interval and divide it by the difference in the x-coordinates.
In this case, the function is f(x) = x + 2^(1/2).
At x = 2, f(2) = 2 + 2^(1/2) = 2 + √2.
At x = 7, f(7) = 7 + 2^(1/2) = 7 + √2.
The average rate of change over the interval [2,7] is:
[f(7) - f(2)] / (7 - 2)
= [(7 + √2) - (2 + √2)] / 5
= (7 - 2) / 5
= 5 / 5
= 1
Therefore, the average rate of change is 1.
Calculate the average rate of change over the interval [2,7] given the function f(x)=x+2−−−−√ . (1 point) Responses The average rate of change is 59 The average rate of change is 5 ninths The average rate of change is 5 The average rate of change is 5 The average rate of change is 15 The average rate of change is 1 fifth The average rate of change is 3
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