Graphing Examples for Lecture.docx
20
f(x) = –2x3 – 3x2 + 12x + 8
f’(x) = –6x2 – 6x + 12
0 = –6(x2 +x – 2)
0 = (x + 2) (x – 1)
16 – 12 – 24 + 8
18
16
14
12
10
8
-2-3+12+8
6
MIN: (–2, –12) & MAX:(1,15)
24-6 => + Smile
4
-12-6 = > - Frown
f”(x) = –12x – 6
0 = –6(2x + 1)  0 = 2x + 1
2
-5
-4
-3
-2
-1
1
0
-2
2
3
4
5
1
2
3
4
-4
1/4 – 3/4 – 6 + 8
-6
IP: (– ½ , 1 ½ )
Y.I: (0,8)
-8
-10
E.B.: As x+∞
As x–∞
f(x)  –∞
f(x)  +∞
↓(–∞,–2)U(1, +∞)
↑(–2,1)
Smile: (–∞,– ½)
Frown: (– ½,+∞)
-12
-14
-16
-18
-20
4
y’ = 3x2 – 3x -6
0 = 3(x2 – x – 2)
0 = (x – 2)(x + 1)
8 – 6 – 12
3
2
1
-1 -3/2 +6
MIN: (2, –10) & MAX:( –1,3 ½ )
12-3 => + Smile
-6-3 = > - Frown
y” = 6x – 3
0 = 3(2x – 1)  0 = 2x – 1
1/8 – 3/8 – 3
IP: (½ , –3 ¼ )
Y.I: (0,0)
E.B.: As x+∞
As x–∞
↓(–1,2)
Smile: (½,+∞)
-6
-5
-4
-3
-2
-1
0
-1
-2
-3
-4
f(x)  +∞
f(x)  –∞
↑(–∞,–1) U(2, +∞)
Frown: (–∞,½)
-5
-6
-7
-8
-9
-10
5