Question

HELP ME WITH CALCULUS 1! I am stuck

Answer 1

answer

graph a

speeds up from (0,1) U (2,3) and slows down from (1,2)

if it marks (2,3) incorrectly, it may be from (2,∞) instead

graph b

speeds up from (1,2) U (3,4) and slows down from (0,1) U (2,3)

if it marks (3,4) incorrectly, it may be from (3,∞) instead

step-by-step explanation

looking at the velocity graphs, when the absolute value of velocity is increasing (moving away from the x axis), the particle must be speeding up. we say absolute value because while velocity has direction, speed only has magnitude, so we need to take the absolute value of velocity to get speed.

for graph a, we can see the velocity moving away from the x axis during the interval (0,1), moving towards the x axis during the interval (1,2) and then moving away again during the interval (2,3)

so it speeds up from (0,1) U (2,3) and slows down from (1,2)

if it marks (2,3) incorrectly, it may be from (2,∞) instead since this is at an endpoint

repeat for graph b where it moves toward the x axis from (0,1), moves away from (1,2), moves towards from (2,3), and moves away again from (3,4)

so it speeds up from (1,2) U (3,4) and slows down from (0,1) U (2,3)

if it marks (3,4) incorrectly, it may be from (2,∞) instead since this is at an endpoint