Monday, October 12, 2015MAT 145 Please review TEST #2 Results and see me with questions, corrections, and concerns.

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Presentation transcript:

Monday, October 12, 2015MAT 145 Please review TEST #2 Results and see me with questions, corrections, and concerns.

Wednesday, October 14, 2015MAT 145

Wednesday, October 14, 2015MAT 145

Wednesday, October 14, 2015MAT 145

Wednesday, October 14, 2015MAT 145

Wednesday, October 14, 2015MAT 145

Monday, October 12, 2015MAT 145 Sketch a continuous function y = f(x) on the closed interval −3 ≤ x ≤ 7, starting at A=(−3,4) and stopping at B=(7,−4). Do not sketch a straight segment!

Monday, October 12, 2015MAT 145 (1)At what x-value locations, if any, on the closed interval −3 ≤ x ≤ 7, does your function y = f(x) reach a maximum? A minimum? (1)At those locations you just identified, what is the value of f ’ (x)? Are there any situations for which that would not be true?

Monday, October 12, 2015MAT 145

Friday, March 14, 2016MAT 145

Friday, March 14, 2016MAT 145

Friday, March 14, 2016MAT 145 Extreme Value Theorem: If f is continuous on the closed interval [a,b] then f attains an absolute maximum value f(c) and an absolute minimum value f(d) at some numbers c and d in [a,b].

Friday, March 14, 2016MAT 145

Friday, March 14, 2016MAT 145

Friday, March 14, 2016MAT 145

Friday, March 14, 2016MAT 145

Friday, March 14, 2016MAT 145

Friday, March 14, 2016MAT 145

Friday, March 14, 2016MAT 145

Monday, October 12, 2015MAT 145

Monday, October 12, 2015MAT 145

Monday, October 12, 2015MAT 145

Monday, October 12, 2015MAT 145

Monday, October 12, 2015MAT 145

Monday, October 12, 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 ….

Monday, October 12, 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.