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2.3 Rates of Change: Velocity and Marginals:Goal: to apply derivatives Average Rate of Change: ,[object Object],change is distance 	change in time
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.
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
Economics: P = R – C		P = total profit, R = total revenue, C = total cost Marginal profit Marginal revenue Marginal Cost

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Rates of change (2)

  • 1.
  • 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