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the graph shows the depth of water w in a reservoir over a one - year period as a function of the number of days x since the beginning of the year. (assume there are 365 days in a year.)
(a) determine the intervals on which the function w is increasing and on which it is decreasing. (enter your answers using interval notation.)
increasing
x
decreasing
x
(b) at what value of x does w achieve a local maximum and a local minimum?
local maximum x=
x
local minimum x = 275
x
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details my notes ask your teacher practice another
this question has several parts that must be completed sequentially. if you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
tutorial exercise
the graphs of four derivatives are given below. match the graph of each function in (a)-(d) with the graph of its derivative in i - iv.

Explanation:

Step1: Analyze increasing - decreasing intervals

For an increasing function, the graph goes up as we move from left - to - right. For a decreasing function, the graph goes down as we move from left - to - right.
From the graph of \(W(x)\), we see that the function \(W\) is increasing on the intervals \([0,100]\cup[250,365]\) and decreasing on the interval \([100,250]\).

Step2: Identify local maximum and minimum

A local maximum occurs where the function changes from increasing to decreasing. A local minimum occurs where the function changes from decreasing to increasing.
The local maximum of \(W\) occurs at \(x = 100\) and the local minimum occurs at \(x=250\).

Answer:

(a) increasing: \([0,100]\cup[250,365]\); decreasing: \([100,250]\)
(b) local maximum \(x = 100\); local minimum \(x = 250\)