4.4 The Fundamental Thorem of Calculus
Example
let ga) = 5" fet) dt
0
2
1 2 00
4
(2)
gis
is on
accumulation suction
u) Fill out the following table:
Χ
023457
"
J(4) 03 435
^g(z) = 5° fet dt
Fundamental Theorem of Calculus (Part I)
f
Ꮧ
If I is continuous on (6) and jos = { tilt, then g is an antibriatie
of f. That is, the [[atet)lt] = f(x)
example cont)
J(x)= { "fct)dt
juss = f(x) < by FTC Part I
gress=fbx)
6) Where is y increasing? Decreasing!
+(x) = g(170 g is increasing on (03) US?)
y is decorsing on (3,5)
fi
,y
-4
14
Cont.
I) Locate the bail extern of y:
g'(x)=0 2=3,5
N=3 is the location of
a bul
bu max: j(3):5
*=5 is the bration of a local min: g(5)=3
1) Where is
J
из
What are the in ectix points?
concave us? Concave dan?
y is conceive
ирк
f is incensing Ex
6,2)0(4.7)
9
concave downs
(84)
down ;
In ection points: (33), (64)
2) Sketch a graph of yagu) on (0.7)
, is decreasing
fl fl
Example
let ga) = 5" fet) dt
0
2
1 2 00
4
(2)
gis
is on
accumulation suction
u) Fill out the following table:
Χ
023457
"
J(4) 03 435
^g(z) = 5° fet dt
Fundamental Theorem of Calculus (Part I)
f
Ꮧ
If I is continuous on (6) and jos = { tilt, then g is an antibriatie
of f. That is, the [[atet)lt] = f(x)
example cont)
J(x)= { "fct)dt
juss = f(x) < by FTC Part I
gress=fbx)
6) Where is y increasing? Decreasing!
+(x) = g(170 g is increasing on (03) US?)
y is decorsing on (3,5)
fi
,y
-4
14
Cont.
I) Locate the bail extern of y:
g'(x)=0 2=3,5
N=3 is the location of
a bul
bu max: j(3):5
*=5 is the bration of a local min: g(5)=3
1) Where is
J
из
What are the in ectix points?
concave us? Concave dan?
y is conceive
ирк
f is incensing Ex
6,2)0(4.7)
9
concave downs
(84)
down ;
In ection points: (33), (64)
2) Sketch a graph of yagu) on (0.7)
, is decreasing
fl fl
