Question

G(x)=-x^2/4+7
What is the average rate of change of g over the interval [-2,4]

Answer 1

-1/2

Explanation:

To find the average rate of change (ARC) of the function g over the interval [-2,4] we need to take the total change in the function value over the interval (which is the difference of its values at the endpoints) and divide it by the length of the interval:

ARC [−2,4] =g(4)-g(-2)/4-(-2)

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Note that this is the same as finding the slope of the line connecting the points on the graph that correspond to the endpoints of the interval:

Answer 2

Explanation:

g(4)=4²/4+7=11

g(-2)=(-2)²/4+7=4/4+7=1+7=8

average rate of change over the interval [-2,4]=(g(4)-g(-2))/4-(-2))

=(11-8)/6

=3/6

=1/2