Question

Find the average rate of change of each function on the interval specified in simplest form. Do not type your answer in factored form and do not type any spaces between characters. g(x)=2x^2-9 on the interval [4,b] The average rate of change is

Answer 1

This expression
`(2b^2 - 48)/(b - 4) \]` represents the average rate of change of g(x) on the interval [4, b].

The average rate of change of a function g(x) over an interval [4, b] is calculated using the formula:

`\[ \text{Average Rate of Change} = (g(b) - g(4))/(b - 4) \]`

For the given function
`\( g(x) = 2x^2 - 9 \)`, let's find g(b) :

`\[ g(b) = 2b^2 - 9 \]`

Now, plug the values into the formula:

`\[ \text{Average Rate of Change} = (2b^2 - 9 - (2(4)^2 - 9))/(b - 4) \]`

Simplify the expression:

`\[ \text{Average Rate of Change} = (2b^2 - 25 - (32 - 9))/(b - 4) \]`

Combine like terms:

`\[ \text{Average Rate of Change} = (2b^2 - 25 - 23)/(b - 4) \]\\ \text{Average Rate of Change} = (2b^2 - 48)/(b - 4)`

This expression represents the average rate of change of g(x) on the interval [4, b].