Let f(t) be the piecewise linear function with domain 0 lessthan or equal to t l

Question

Let f(t) be the piecewise linear function with domain 0 lessthan or equal to t lessthan or equal to 8 shown in the graph below (which is determined by connecting the dots). Define a function A(x) with domain 0 lessthan or equal to x lessthan or equal to 8 by A(x) = integral _0^z f(t) dt. Notice that A(x) is the net area under the function f(t) for 0 lessthan or equal to t lessthan or equal to x. If you click on the graph below a full-size picture of the graph will open in another window. (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=

Explanation / Answer

Increasing from (2,5]

Decreasing from [1,2)union[6,7]

Max value at x=5

Min value at x=2

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