Question

How do you find the average rate of change of `y=x^2-3x` from 2 to 5?

Answer 1

The average rate of change (in `y`) is `color(red)(4)` (for each unit change in `x`)

Explanation:

Given
`color(white)("XXX")y_x = x^2-3x`

`y_5 = 5^2-3*(5) =10`

`y_2 = 2^2-3*(2) = -2`

The change in `y` fromn `2` to `5` is
`color(white)("XXX")Delta y = 10 -(-2) = 12`

The interval from `2` to `5` has a width of
`color(white)("XXX")Delta x = 5-2 = 3`

The average rate of change is
`color(white)("XXX")(Delta y)/(Delta x) = 12/3 = 4`