Question

Find the average rate of change of the function from
`x_(1)`= 1 to
`x_(2)` = 5.​

Function =
`x^(2)` - 4x + 10

Answer 1

Hi there!

`\large\boxed{\text{Average rate} = 2}`

Use the following equation to solve:

`\text{Average rate} = (f(x_(2)) - f(x_(1)))/(x_(2) - x_(1))`

Solve for the y-values of the equation at the given x values:

f(1) = 1² - 4(1) + 10 = 7

f(5) = 5² - 4(5) + 10 = 15

Plug the solved values into the equation:

`\text{Average rate} = (15 - 7)/(5-1)`

Simplify:

`\text{Average rate} = (8)/(4) = 2`