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Given the function g(x)=x²-9x+18, determine the average rate of change of the function over the interval 0<=x<=8

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Final answer:

To determine the average rate of change of the function g(x)=x²-9x+18 over the interval 0<=x<=8, find the difference in function values at the endpoints and divide by the difference in x-values.

Step-by-step explanation:

To determine the average rate of change of the function g(x)=x²-9x+18 over the interval 0<=x<=8, you need to find the difference between the function values at the endpoints of the interval and divide by the difference in x-values.

First, evaluate g(8) by substituting x=8 into the function: g(8) = 8²-9(8)+18 = 42.

Then, evaluate g(0) by substituting x=0 into the function: g(0) = 0²-9(0)+18 = 18.

The average rate of change is the difference in the function values divided by the difference in x-values: (42-18)/(8-0) = 24/8 = 3.

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