Find the average rate of change of g (x) = -2x^2-2x from x=2 to x=4
Simplify your answer as much as possible.
To find the average rate of change of a function, we use the formula:
Average rate of change = (g(b) - g(a)) / (b - a)
In this case, a = 2 and b = 4. Plugging these values into the formula:
Average rate of change = (g(4) - g(2)) / (4 - 2)
First, compute g(4):
g(4) = -2(4)^2 - 2(4)
g(4) = -2(16) - 8
g(4) = -32 - 8
g(4) = -40
Next, compute g(2):
g(2) = -2(2)^2 - 2(2)
g(2) = -2(4) - 4
g(2) = -8 - 4
g(2) = -12
Now, plug these values back into the formula:
Average rate of change = (-40 - (-12)) / (4 - 2)
Average rate of change = (-40 + 12) / 2
Average rate of change = -28 / 2
Average rate of change = -14
Therefore, the average rate of change of g(x) = -2x^2-2x from x=2 to x=4 is -14.