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Alexxandr [17]
3 years ago
7

Please help I don’t understand this.

Mathematics
1 answer:
tresset_1 [31]3 years ago
3 0

The average rate of change of <em>g(x)</em> over the interval [2, 8] is given by

(<em>g</em> (8) - <em>g</em> (2)) / (8 - 2)

In other words, it's the slope of the line through the points (2, <em>g</em> (2)) and (8, <em>g</em> (8)).

Use the definition of the function to evaluate it at the points in the numerator:

• 8 ≥ 4, so using the second piece, <em>g</em> (8) = -0.5(8) + 8 = 4

• 2 < 4, so <em>g</em> (2) = 5(2) + 1 = 11

Then the average rate of change is

(<em>g</em> (8) - <em>g</em> (2)) / (8 - 2) = (4 - 11) / 6 = -7/6

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