Objective 1b - Increasing/Decreasing
1) inc. x<-2
dec. -2 < x
rel. max(-2,3)

2) inc. -3 < x < 1
dec. x<-3, 1 < x
max(1,5), min (-3,1)

3) inc. x<0, 1 < x < 3
dec. 0 < x < 1, 3 < x
max(0,4)(3,5), min(1,2)

4) inc. 1 < x < 3
dec. x<1,x>3
max(3,3), min(1,-2)

5) inc. 3/2 < x
dec x<3/2
dec. x<0 min(1.5,1.75)

6) inc. -1 < x
dec. x<-1
min (-1,-1)

7)inc. x<-5/2, 5/2 < x
dec. -5/2 < x < 5/2
max(-2.5,155), min(2.5, -95)

8)inc. -3 < x < 0, x>3
dec. x<-3, 0 < x < 3
max(0,3), min(-3,-78)(3,-78)

9) inc. x<-3, 0 < x < 1
dec. -3 < x < 0, 1 < x
max (-3,145) (1,17), min (0,10)

10) inc. x>0
dec x<0
min (0,2)

Objective 2a - Concave Up/Down

2a) conave down
b) concave up

3)a) concave down
b) concave up

Objective 2b - Concave Up/Down

2) concave up: x<-1
concave down: x>-1
inf. pt. when x=-1

3) concave up: 1/2 concave down: x<1/2, x>2
inf. pt. when x=1/2, x=2

4) concave down: x<1, x>1
no inflection point

5) concave up for all x
no inflection point

6) concave up: x<-2/3, x>0
concave down: -2/3 inf. pt. when x=-2/3, x=0

7) concave up: x>0
concave down: x<0
inf. pt. when x=0

8) concave up: x< -sqrt(3), x> sqrt(3)
concave down: -sqrt(3) inf. pt when x= -sqrt(3), x= sqrt(3)

#9-12 (on your own)

Objective 2c - Concave Up/Down
(The graphs are on your own)
1)a) x<-4, x>2
b) -4 c) (2,-28)
d) (-4,80)
e) x>-1
f) x<-1
g) (-1,26)

2)a) x>3
b)x<3
c)(3,-24)
d) none
e)x<0,x>2
f)0 g)(0,0) (2,-13)

3)a) x<0, x>2
b) 0 c) (2,-4)
d) (0,0)
e) x>1
f) x<1
g) (1,-2)

Objective 3 - Grouping Rational Functions

1) y=6/7
) y=-1/8
3) y=7/5
4) y=0
5)x=4, x=-3
6)x=2, x=-2, x=1, x=-1
7) V.A. x=5
H.A. y=0
(graph on your own)

8) V.A. x=3, x=-3
H.A. y=1
(graph on your own)

9) V.A. x=6
H.A. y=1
(graph on your own)

10) V.A,. x=2, x=-2
H.A. y=0
(graph on your own)

Objective 4 - Min/Max Applications

1) x=12, y=56
2) t=3, i=13A

4) Max(0,1) because f''(0)=-16<0
min(1,-2) because f''(1)=20>0 and
(-4,-127) because f''(-4)=80>0

5) 150 yds by 600 yds
(max area =lw where l+4w=1200 yds)

Objective 5 Differentials

Unit 4 Outline