Find the average rate of change of g (x) = -3x^2 + 4 from x = -4 to x = 1.
Simplify your answer as much as possible.
To find the average rate of change of a function over an interval, we need to calculate the change in the value of the function over that interval and divide it by the change in the value of x.
First, we need to calculate the value of g at x = -4 and x = 1:
g(-4) = -3(-4)^2 + 4 = -3(16) + 4 = -48 + 4 = -44
g(1) = -3(1)^2 + 4 = -3(1) + 4 = -3 + 4 = 1
Next, we calculate the change in the value of g over the interval from x = -4 to x = 1:
g(1) - g(-4) = 1 - (-44) = 45
The change in the value of x over the interval is:
1 - (-4) = 5
Therefore, the average rate of change of g from x = -4 to x = 1 is:
(1 - (-44)) / (1 - (-4)) = 45 / 5 = 9
So, the average rate of change of g from x = -4 to x = 1 is 9.