A particle moves along a straight line. The graph of the particle's position x(t) at time t is shown below for 0 < t < 6. The graph has horizontal tangents at t = 1 and t = 5 and a point of inflection at t = 2. a) On what interval is the velocity of the particle increasing? Complete the inequality below. 0 < t < 2 b) At what values of t is the particle at rest? t = 1 and t = 5
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The slope of the tangent line is increasing on the intervals where the graph of the position function is concave up. Looking at the graph, we can see that the graph is concave up on the intervals (1, 2) and (5, 6). Show more…
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