Friday, February 19, 2016MAT 145. Friday, February 19, 2016MAT 145.

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Presentation transcript:

Friday, February 19, 2016MAT 145

Friday, February 19, 2016MAT 145

Friday, February 19, 2016MAT 145

Friday, February 19, 2016MAT 145

Friday, February 19, 2016MAT 145

Friday, February 19, 2016MAT 145

Friday, February 19, 2016MAT 145

Friday, February 19, 2016MAT 145 Now apply this to other log functions:

Friday, February 19, 2016MAT 145

Friday, February 19, 2016MAT 145

Friday, February 19, 2016MAT 145 And extend this to other functions:

Friday, February 19, 2016MAT 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. 1.Calculate the rabbit’s velocity and acceleration functions over the interval from 0 to 6 seconds. 2.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. 3.Determine when the rabbit is speeding up and when it is slowing down. Explain your response with justification.

Friday, February 19, 2016MAT 145

Friday, February 19, 2016MAT 145

Friday, February 19, 2016 MAT 145

Friday, February 19, 2016MAT 145

Friday, February 19, 2016MAT 145

Friday, February 19, 2016MAT 145 A particle moves on a number line with its position given by such that s(t) is measured in cm and t in seconds. 1. Determine the particle’s velocity and acceleration functions and then sketch graphs of position, velocity, and acceleration on the interval from 0 to 6 seconds. 2. Determine the times from 0 to 6 seconds when the particle is moving to the right, when it is moving to the left, and when it is at rest. Use interval notation or inequality notation. Explain and justify your response. 3. Determine when the particle is speeding up and when it is slowing down. Use interval notation or inequality notation. Explain and justify your response.

Monday, February 22, 2016MAT 145 Differentiate implicitly. Take nat. log of both sides. Use log properties. Solve for y’. Substitute and simplify.