Find the average rate of change of g(x)=1x^3+3 from x=-2 to x=2
To find the average rate of change of g(x) from x = -2 to x = 2, we need to calculate the change in the function's value over that interval and divide by the change in the input.
First, we find the value of g(x) at x = -2 and x = 2:
g(-2) = 1(-2)^3 + 3
g(-2) = 1(-8) + 3
g(-2) = -8 + 3
g(-2) = -5
g(2) = 1(2)^3 + 3
g(2) = 1(8) + 3
g(2) = 8 + 3
g(2) = 11
Next, we calculate the change in the function's value over the interval:
Change in g(x) = g(2) - g(-2)
Change in g(x) = 11 - (-5)
Change in g(x) = 16
Finally, we calculate the average rate of change:
Average rate of change = Change in g(x) / Change in x
Average rate of change = 16 / (2 - (-2))
Average rate of change = 16 / 4
Average rate of change = 4
Therefore, the average rate of change of g(x) = x^3 + 3 from x = -2 to x = 2 is 4.