The average rate of change of the function from x == -4 to x = 3 is calculated as: -26.
The formula for determining the average rate of change across a given interval of a function is expressed as:
Average rate of change = g(b) - g(a)/b - a.
Given the function, g(x) = -2x³ + 5 to find the average rate of change from x = -4 to x = 3, do the following:
a = -4
g(a) = g(-4) = -2(-4)³ + 5 = -2(-64) + 5 = 128 + 5 = 133
b = 3
g(b) = g(3) = -2(3)³ + 5 = -2(27) + 5 = -54 + 5 = -49
Substitute the values into g(b) - g(a)/b - a:
Average rate of change = (-49 - 133)/(3 - (-4))
Average rate of change = -182/7
Average rate of change = -26
Thus, the average rate of change of the function from x == -4 to x = 3 is calculated as: -26.
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