Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 10 - Section 10.5 - Derivatives: Numerical and Graphical Viewpoints - Exercises - Page 753: 36d

Answer

B

Work Step by Step

The slope of the tangent line through the point on the graph of $f$ where $x=a$ is given by the instantaneous rate of change, or derivative $m_{tan}=$ slope of tangent = instantaneous rate of change = derivative $=f^{\prime}(a)$ --------------- At x=0 the slope of the tangent is negative (the function decreases as we move to the right) Tracing the graph from x=0 to the right, to x=200, we note that the tangents never break the horizontal, that is, the tangents are always descending, with negative slope. So, our choice is B.
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