3.3 –Differentiation Rules REVIEW: Use the Limit Definition to find the derivative of the given function.

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Presentation transcript:

3.3 –Differentiation Rules REVIEW: Use the Limit Definition to find the derivative of the given function.

3.3 –Differentiation Rules What are the rules?

3.3 –Differentiation Rules

3.4 –The Derivative as a Rate of Change Position, Displacement, Velocity, Speed, and Acceleration Position: the location of an object as determined by a position function. Displacement: the distance an object is away from its initial position after travelling for a certain interval of time. 5 feet 3 feet 1 foot

3.4 –The Derivative as a Rate of Change Position, Displacement, Velocity, Speed, and Acceleration Position: the location of an object as determined by a position function. Displacement: the distance an object is away from its initial position after travelling for a certain interval of time. 9 feet 5 feet 1 foot

3.4 –The Derivative as a Rate of Change Position, Displacement, Velocity, Speed, and Acceleration Position: the location of an object as determined by a position function. Displacement: the distance an object is away from its initial position after travelling for a certain interval of time.

3.4 –The Derivative as a Rate of Change Position, Displacement, Velocity, Speed, and Acceleration Velocity: the change in position with respect to a change in time. It is a rate of change with direction. Speed: the absolute value of velocity. It is a rate of change without direction.

3.4 –The Derivative as a Rate of Change Position, Displacement, Velocity, Speed, and Acceleration Acceleration: the change in velocity with respect to a change in time. It is a rate of change with direction.

3.4 –The Derivative as a Rate of Change Economics Marginal cost of production: the rate of change of costs with respect to the level of production. Cost of production: a function of the units produced (x) that generates the cost of producing those units. Average cost of production: the cost of production function divided by the number of units produced at that cost. Marginal cost is an approximation of the cost to produce one more unit after producing x units

3.4 –The Derivative as a Rate of Change Economics Cost of production: Find the average cost in producing 50 units. Find the marginal cost to produce the 51 st unit. Find the actual cost to produce the 51 st unit.

3.4 –The Derivative as a Rate of Change