Lat / a) be the eco se l car tunction with doman 0 ? so n n the graph below \' w

Question

Lat / a) be the eco se l car tunction with doman 0 ? so n n the graph below ' which cac nad by oor nocn g the dots, Dotna a tunction A 2] with doman U ? by Notce thet A ,ja the net res rder t he unction for If you cí k on the graph below. ? full-see pet ure of the ?8ph wil open in 8nother window , 1S A Find the elewing vaues of the uneticn A) A(C) 412)-1 A(4)-0 e use terval notat on to n cate ther terval Or Lnon cf ntras where A z)s nores mand decreas ng A(») isinoreasing for in the interval | lo (,) is decreasing for P ?n the imenal | [341.[5? C) Find aer has is macimum and minimum values

Explanation / Answer

We have to find the areas here....

A(0) = integral from 0 to 0 f(t)dt = ZERO --> ANS

A(1) :
Area between x = 0 to x = 1 which is 1/2*b*h
= 1/2*1*-4
= -2

A(2) :
-2 + 1/2*b*h
-2 + 1/2*1*1
-2 + 1/2
= -1.5

A(3) :
-1.5 + 1/2*b*h (area between 2 to 3)
-1.5 + 1/2*1*1
-1.5 + 0.5
-1

A(4) :
-1

A(5) :
-1 + 1/2*1*-2
-1 - 1
=-2

A(6) :
-2 + (area of trpzd from 5 to 6)
-2 + 1*(-2-3)/2
-2 - 5/2
-4.5

A(7) :
-4.5 + -5/2
- 7

A(8) :
-7 + 1/2*b*h
-7 + 1/2*1*-2
-8

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B)
A inc :
This happens whenever A is positive,

So, (1,3)

Decreasing :
(0,1) U (4,8)

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C)
max : Clearly when x = 0
min : Clearly when x = 8

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