2. The Instantaneous Rate of Change:the instantaneous rate of change or simply rate of change of y = ƒ(x) at x is the limit of the average rate of change on the interval [x, x + Δx], as Δx approaches 0. If y is a distance and x is time, then the rate of change is a velocity.
3. The Position Function:For a free-falling object: h = -16t2 + v0t + h0 his the height in feet , t is time in seconds, v0 is initial velocity, ho is initial height in feet The Velocity Function:For a free-falling object: h’ = -32t + v0 t is time in seconds, v0 is initial velocity
4. Economics: P = R – C P = total profit, R = total revenue, C = total cost Marginal profit Marginal revenue Marginal Cost
![2.3 Rates of Change: Velocity and Marginals:Goal: to apply derivatives Average Rate of Change: ,[object Object],change is distance change in time](https://image.slidesharecdn.com/ratesofchange-101207112024-phpapp02/85/rates-of-change-1-320.jpg)
![The Instantaneous Rate of Change:the instantaneous rate of change or simply rate of change of y = ƒ(x) at x is the limit of the average rate of change on the interval [x, x + Δx], as Δx approaches 0. If y is a distance and x is time, then the rate of change is a velocity.](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)