Question

What is the average rate of change for the function g(x) between 3 and 7. Show your work. g(x) = 8x2 - 7x + 2

Answer 1

73

Step-by-step explanation:

The average rate of change for the function g(x) between a and b can be calculated as:

`(g(b)-g(a))/(b-a)`

So, if a = 3 and b = 7, we first need to calculate g(3) and g(7):

`\begin{gathered} g(x)=8x^2-7x+2 \\ g(3)=8(3)^2-7(3)+2 \\ g(3)=8(9)-21+2 \\ g(3)=72-21+2 \\ g(3)=53 \end{gathered}`
`\begin{gathered} g(7)=8(7)^2-7(7)+2 \\ g(7)=8(49)-49+2 \\ g(7)=392-49+2 \\ g(7)=345 \end{gathered}`

Now, the average rate of change is equal to:

`(g(7)-g(3))/(7-3)=(345-53)/(4)=(292)/(4)=73`

Therefore, the average rate of change of g(x) between 3 and 7 is 73.