Question

How do you find the intervals of increasing and decreasing using the first derivative given `y=x^2-6x+8`?

Answer 1

See below

Explanation:

`y'=2x-6`

`y'=0` at `x=3`

For `x < 3`, `y'` is negative (for example at `x=1`, `y'=-4`)
so `y` is decreasing on the interval `(-oo,3)`

For `x > 3`, `y'` is positive (for example at `x=4`, `y'=2`)
so `y` is increasing on the interval `(3,oo)`