The average rate of change obtained from the ratio of the change in y to the change in x is 39.
The average rate of change can be obtained using the relation :
Rate of change = (y2 - y1) ÷ (x2 - x1)
At ; x1 = 1
y1 can be calculated from the function ;
y1 = 3(1³) + 1 = 3(1) + 1 = 4
At ; x2 = 3
y1 can be calculated from the function ;
y2 = 3(3³) + 1 = 3(27) + 1 = 82
Rate of change can be calculated thus :
Slope = (82 - 4) ÷ (3 - 1) = 78 ÷ 2 = 39
Therefore, the average rate of change is 39.
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