The average rate of change of a function over an interval is the change in the function divided by the change in the independent variable (x) over that interval.
To find the average rate of change of f(x) = 2x^2 over the interval [-3,4], we first need to find the change in the function over that interval.
f(4) - f(-3) = 2(4)^2 - 2(-3)^2 = 32 - 18 = 14
Next, we need to find the change in x over the interval:
4 - (-3) = 7
So, the average rate of change of f(x) over the interval [-3,4] is:
14/7 = 2
To find the average rate of change of g(x) = 3x^2 over the same interval, we follow the same steps:
g(4) - g(-3) = 3(4)^2 - 3(-3)^2 = 48 - 27 = 21
4 - (-3) = 7
So, the average rate of change of g(x) over the interval [-3,4] is:
21/7 = 3
Therefore, the average rate of change of f(x) over the interval [-3,4] is 2, and the average rate of change of g(x) over the same interval is 3.