Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 13 - Section 13.3 - Tangent Lines and Derivatives - 13.3 Exercises - Page 923: 46

Answer

(a) The initial velocity of the car is close to zero. (b) The car was going faster at C. (c) The car was slowing down at B, but was speeding up at A and C. (d) the car was stopped between D and E.

Work Step by Step

(a) The initial velocity of the car is close to zero as the slope of the tangent line when $t=0$ is close to zero. (b) The car was going faster at C because the slope (representing speed) of the tangent line at point C is larger than that at point B. (c) The car was slowing down at B, but was speeding up at A and C. This can be determined by the trend of the slopes of tangent lines immediately after each point. (d) The slopes of the tangents between D and E are zero, indicating that the speed was zero in this region. In other words, the car was stopped between D and E.
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