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

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

a) [6,8],

b) [-4,4]

**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 [6,8], the average rate of change is as follows.

444

Thus , the average rate of change of the function 3x^{3} + 3 over the interval [2,4]is 444.

b) For the function 3x^{3} + 3 and interval [-4,4]

48

Thus, the average rate of change of the function 3x^{3} + 3 over the interval [-2 , 2] is 48.