Question

Please help!!!!

what is the average rate of change of the function g(x) = 3(2x) - 6 over the interval [0,3]? Show all work.

Answer 1

The average rate of the function g(x)=6

Explanation:

We are given that a function
`g(x)=3(2x)-6` on the interval [0,3]

We have to find the value of rate of change of the given function over the interval [0,3]

To find the value of average rate of change of the function we apply slope formula

Average rate=Slope=m=
`(y_2-y_1)/(x_2-x_1)`

Let a=0, b=3

Now,
`g(a)=3(2\cdot0)-6=-6`

g(b)=
`3(2\cdot3)-6=18-6=12`

Now, the average rate of the function g(x)=
`(g(b)-g(a))/(b-a)`

Average rate of the function g(x)=
`(12-(-6))/(3-0)`

Average rate of the function g(x)=
`(18)/(3)=6`

Hence, the average rate of the function g(x)=6

Answer :6

Answer 2

The average rate of change (m) of function g(x) on interval [a, b] is given by

... m = (g(b) -g(a))/(b -a)

Here, we have

• g(3) = 723
• g(0) = -5

so the average rate of change is

... m = (723 -(-5))/(3 - 0) = 728/3 = 242 2/3