Friday, October 23, 2015MAT 145 Please review TEST #2 Results and see me with questions.

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Presentation transcript:

Friday, October 23, 2015MAT 145 Please review TEST #2 Results and see me with questions.

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145 dynamic view on YouTube

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145 For h(x) shown below, use calculus to determine and justify: All x-axis intervals for which h is increasing All x-axis intervals for which h is decreasing The location and value of every local & absolute extreme. All x-axis intervals for which h is concave up All x-axis intervals for which h is concave down The location of every point of inflection and all asymptotes. Finally, use all this info to sketch a graph of h!

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145 m a t h

Friday, October 23, 2015MAT 145 Here’s a graph of g’(x). Determine all intervals over which g is increasing and over which g is decreasing. Identify and justify where all local extremes occur.

Friday, October 23, 2015MAT 145 Here’s a graph of h”(x). Determine all intervals over which h is concave up and over which h is concave down. Identify and justify where all points of inflection occur.

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT 145

Friday, October 23, 2015MAT An object is moving in a positive direction when …. 2.An object is moving in a negative direction when …. 3.An object speeds up when …. 4.An object slows down when …. 5.An object changes directions when …. 6.The average velocity over a time interval is found by …. 7.The instantaneous velocity at a specific point in time is found by …. 8.The net change in position over a time interval is found by …. 9.The total distance traveled over a time interval is found by ….

Friday, October 23, 2015MAT An object is moving in a positive direction when v(t) > 0. 2.An object is moving in a negative direction when v(t) < 0. 3.An object speeds up when v(t) and a(t) share same sign. 4.An object slows down when v(t) and a(t) have opposite signs. 5.An object changes directions when v(t) = 0 and v(t) changes sign. 6.The average velocity over a time interval is found by comparing net change in position to length of time interval (SLOPE!). 7.The instantaneous velocity at a specific point in time is found by calculating v(t) for the specified point in time. 8.The net change in position over a time interval is found by calculating the difference in the positions at the start and end of the interval. 9.The total distance traveled over a time interval is found by first determining the times when the object changes direction, then calculating the displacement for each time interval when no direction change occurs, and then summing these displacements.