Find the average rate of change of the function over the given intervals.

f (x) = 3x^{3} + 3,

a) [2,4],

b) [-2,2]

**Solution:-**

a) The average rate of change of a function f(x) over the interval

[x_{1} , x2] is as follows.

For the function f(x) = 3x^{3} + 3 and interval [2,4], the average rate of change is as follows.

84

Thus , the average rate of change of the function 3x^{3} + 3 over the interval [2,4]is 84.

b) For the function 3x^{3} + 3 and interval [-2,2]

12

Thus, the average rate of change of the function 3x^{3} + 3 over the interval [-2 , 2] is 12.