Calculus I (MAT 145) Dr. Day Wednesday March 6, 2019

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Presentation transcript:

Calculus I (MAT 145) Dr. Day Wednesday March 6, 2019 Related Rates (3.9) See handout. Upcoming Material: Chapter 4 Absolute and Relative Extremes Increasing and Decreasing Behavior of Functions Connecting f and f’ Concavity of Functions: A function’s curvature Connecting f and f” Graphing a Function: Putting it All together! Max-Mins Problems: Determine Solutions for Contextual Situations Wednesday, March 6, 2019 MAT 145

Related Rates (3.9) Illustrations and Examples Temple University RR site (discussion and animation) Kelly’s RR notes (solutions and animations) More Temple University animations Paul’s Online Math Notes: RR (worked examples) In-class Examples Wednesday, March 6, 2019 MAT 145

A rabbit moves within a straight horizontal tube according to the position function such that s(t) is measured in feet and t in seconds. When s(t) is positive, the rabbit is to the right of some arbitrary point labeled 0. Calculate the rabbit’s velocity and acceleration functions over the interval from 0 to 6 seconds. Determine the times from 0 to 6 seconds when the rabbit is moving to the right and when it is moving to the left. Explain your response with justification. Determine when the rabbit is speeding up and when it is slowing down. Explain your response with justification. Solution Guide Wednesday, March 6, 2019 MAT 145

Position, velocity, acceleration Velocity: rate of change of position Acceleration: rate of change of velocity Velocity and acceleration are signed numbers. Sign of velocity (pos./neg.) indicates direction of motion (right/left or up/down) When velocity and acceleration have the same sign (both pos. or both neg.), then object is speeding up. This is because object is accelerating the same direction that the object is moving. When velocity and acceleration have opposite sign (one positive and one negative), then object is slowing down. This is because object is accelerating the opposite direction that the object is moving. Wednesday, March 6, 2019 MAT 145

Wednesday, March 6, 2019 MAT 145

Wednesday, March 6, 2019 MAT 145