Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 2 - Section 2.3 - Getting Information from the Graph of a Function - 2.3 Exercises - Page 181: 59

Answer

a) The intervals when the function is increasing are (0, 150) and (300, 400). The interval when the function is decreasing is (150, 300). b) W achieves a local maximum at $x=150$ and a local minimum at $x=300$. c) The net change is -50 ft

Work Step by Step

a) A function decreases when the slope is negative. While a function increases when the slope is positive. b) The local maximum values are all those that are at the top of crests that forms in functions (if any). While the local minimum values are all those that are at the bottom of where U-shaped parts are formed (if any). c) First, we find both values which will be $W(100)=75$ ft and $W(300)=25$ ft, then we subtract the first one from the second one: $W(300)−W(100)=25−75=-50$ ft. The answer is negative since the depth the water in the reservoir decreased from 100 days to 300 days.
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