Question
Let f(t) be the piecewise linear function with domain 0 <t < 8 shown in the graph below (which is determined by
connecting the dots). Define a function A(x) with domain 0 <x < 8 by
:| f(1) dt.
A(x)
Notice that A(x) is the net area under the function f(t) for 0 < t < x. If you click on the graph below, a full-size picture of the
graph will open in another window.
1.0
4,0
F1
-5
Graph of y = f(t)
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Transcribed Image Text:Let f(t) be the piecewise linear function with domain 0 <t < 8 shown in the graph below (which is determined by connecting the dots). Define a function A(x) with domain 0 <x < 8 by :| f(1) dt. A(x) Notice that A(x) is the net area under the function f(t) for 0 < t < x. If you click on the graph below, a full-size picture of the graph will open in another window. 1.0 4,0 F1 -5 Graph of y = f(t)
(A) Find the following values of the function A(x).
A(0) =
A(1) =
A(2) =
A(3) =
A(4) =
A(5) =
A(6) =
A(7) =
A(8) =
(B) Use interval notation to indicate the interval or union of intervals where A(x) is increasing and decreasing.
A(x) is increasing for x in the interval
A(x) is decreasing for x in the interval
(C) Find where A(x) has its maximum and minimum values.
A(x) has its maximum value when x =
A(x) has its minimum value when x =
expand button
Transcribed Image Text:(A) Find the following values of the function A(x). A(0) = A(1) = A(2) = A(3) = A(4) = A(5) = A(6) = A(7) = A(8) = (B) Use interval notation to indicate the interval or union of intervals where A(x) is increasing and decreasing. A(x) is increasing for x in the interval A(x) is decreasing for x in the interval (C) Find where A(x) has its maximum and minimum values. A(x) has its maximum value when x = A(x) has its minimum value when x =
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