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. A(x)=∫0x f(t)dt. Notice that A(x) is the net area under the function f(t) for 0≤t≤x (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=
Let f(t) be the
A(x)=∫0x f(t)dt.
Notice that A(x) is the net area under the function f(t) for 0≤t≤x
(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=
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images