3.4 Velocity and Other Rates of Change

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Presentation transcript:

3.4 Velocity and Other Rates of Change Today we will study and understand the derivative as a rate of change of a function.

What other words can be used for derivative? Slope of tangent Instantaneous rate of change Velocity Speed Increase or decrease of a quantity with respect to another quantity

Enlarging Circles (increase of a quantity with respect to another quantity)

Notation for particle motion:

For motion on a line, what is the relationship between velocity and speed?

Studying Particle Motion – without a calculator A particle moves along the x-axis so that at time t its position is given by What is the velocity of the particle at any time t? During what time intervals is the particle moving to the left? Justify your answer. c. At what time on [0, 3] is the particle moving fastest? Justify your answer. d. At what time on [0, 4] is the particle moving fastest? Justify

Studying Particle Motion – on a calculator… A particle moves along the x-axis so that at time t its position is given by What is the velocity of the particle at any time t? b. During what time intervals is the particle moving to the left? Justify your answer. c. At what time on [0, 1.4] is the particle moving fastest? d. At what time on [0, 2.5] is

Assignment: 3.4A: p.135: 1, 19, 23, 27 (read Example on p. 134) Study for Quiz #5, Sections 3.1-3.3