Class notes APPM 1350 Unit 3.4

3.4 Curve Sketching
Example: fas: 304
Al Domain: (100,-2) U(-2, 2) U(2,00)
B) Intercepts: y-int: 3601
() x):
M
(x3)-4
3K
by t: 0=-xx
(0,0)
>= f(x) f(x)= odd
0) Agamototes: Horizontal: . E
223×
(00)
Tim Sx
1832 x24=-00
3X
Vertical: 1 in 3x
lin
0
HA 0)
X700
Wc us x 2, 360-06 and
×2405
2
"@y=O) Wc un x
We un x approaches
2 from the right, 3x-16
and x²-4 10
←
f is old and lim
Lin
x + 1 2. f(x) = .00
Life wise X f(x)=
VAs of x9±2
X+2°
fax)=rge, than




fi

,3.4 Cont.
E) Internals Inc/Dec
3x
f(x) = f ( 3 ) = ( +_ _AX(s) (3x)(2+)
2
༤
(+34)2
-3x²-12
(x²-4)²
=-3(844)
20
on
the darwin of f
(8-4)2
So f is decessing on (-00,-2)0€2,2)U8,00)
F| Local Extrema
No critical #s, so there we no local extrema
た
Note: += ±2 are not critical numbers Yc they
the lomain.
6) Concavityl In ection
we not in
f(x) = d(-3x²-12.) = (x² <3) (-6x) - (-3-212) (261= 1) 2)
(x² 2)<
4) 2x (-3(624) + (3x312).2]
2
(x²-4)³
2x (3x²+36)
(424)
2_4]
3
=6x√(x²+12) +
(x²-4)³
り
t
*" (x)=0 when x=0
(" (3) ONE" When x= £2




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