Some points not to be overlooked. Don't trust me on these. Think to yourself "does that make sense" and then ask me if it doesn't.
If the rate of change of 𝑓𝑥 is positive on the interval 𝑎,𝑏, then 𝑓𝑥 is increasing on that interval.
If the rate of change of 𝑓𝑥 is negative on the interval 𝑎,𝑏, then 𝑓𝑥 is decreasing on that interval.
If the rate of change of 𝑓𝑥 is constant everywhere on the interval 𝑎,𝑏, then over that interval 𝑓𝑥 is linear.
If the rate of change of 𝑓𝑥 is 0 everywhere on the interval 𝑎,𝑏, then over that interval 𝑓𝑥 is constant