2.3 Rates of Change: Velocity and Marginals

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2.3 Rates of Change Velocity and Marginals
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Two Primary applications of Derviatives

• Slope The derivative of f is a function that
  gives the slope of the graph of f at a point
  (x,f(x)).
• Rate of Change The derivative of f is a function
  that gives the rate of change of f(x) with
  respect to x at the point (x,f(x)).

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Definition of Average Rate of Change
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Average Velocity
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The average velocities are negative when the
object is moving downwards.
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Definition of Instantaneous Rate of Change
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The general position function for a free-falling
object, neglecting air resistance.
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Marginal Profit, Marginal Revenue, and Marginal
Cost
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Profit Revenue - Cost
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Demand function

• The number of units x that consumers are willing
  to purchase at a given price per unit p is given
  by the demand function.
• Demand function p f(x)
• Notice p is lower case.

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Revenue Function

• The total revenue R is related to the price per
  unit (p) and the quantity demanded (x) (or sold).
• Revenue function R xp.

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