, 8.
naverage
·
igradient
· cimis
*
~iteminatives
·firstprinciple
*
8t
rules
, ·
rouersorge recient
same as the
single gradiento fa straight
line bow the 2 points
12 points)
bits the curre
↳
little to remove this
of lots of
justcalculate
·
gradients
to If
A.G. is the gradientofa straight line
passing through a points on a curve [ 3; 4] - inclusive
↳ it interval end
make sure to call
average gradient -
a values
↳nota n ordered
pair
I
AG
yz y,
= -
xz
-
3,
& rate of
average change average gradient points
-
-
2
& instantaneous
r a te of derivative
change
=
example ↳
tangent=1 point
f(x) -
= 3(x) (x) +
Determine:a ) AGbetween (1-2) and (0,0) b) AGbetween ec=-3 and x 4 =
AG= 0 2 +
(- 5; -
50)(4; 44) -
0 -
1
AG:
2
Y5c
--
↳ve=o n decreasing side parabola
of
44 30+
=
-
4 5
+
=-
2
c) AGbetween (2; f(z) and (3;f(3)
(2; -10) (3; -24)
AG y2 -y)
=
32 -31
24 10 +
=-
3-2
=
14
-
=
St di AG between (c;fle)) and locth;f(ecth))
↳
can'tfindnumerical values:
use
directly as points
AG yz y)
= -
32 -
6C1
f(x h) + - f(x) ->
firstprinciple
-
↳
finds the formula
H
general on
any graph
3(x h)2 (x h) ) -
3x2 x) ↳
fill in actual graphs
+ - +
+
- +
-
R
3(x2 zech n2) (x h) 3x2 -
x
-
aim is to cancel outh in denominator
-
+ + +
+ +
-
h
=-C2-beck-shth32
H
-
back -
k -
342
=>
H
k) -
bx -
1 -
3h)
=>
k
=- 66-5-1) general
formula ofaverage gradient
usedin a hence question to sub in
I
x= first (smallestgiven so values
h distancebtwec-values:(x2 -x.)
=
naverage
·
igradient
· cimis
*
~iteminatives
·firstprinciple
*
8t
rules
, ·
rouersorge recient
same as the
single gradiento fa straight
line bow the 2 points
12 points)
bits the curre
↳
little to remove this
of lots of
justcalculate
·
gradients
to If
A.G. is the gradientofa straight line
passing through a points on a curve [ 3; 4] - inclusive
↳ it interval end
make sure to call
average gradient -
a values
↳nota n ordered
pair
I
AG
yz y,
= -
xz
-
3,
& rate of
average change average gradient points
-
-
2
& instantaneous
r a te of derivative
change
=
example ↳
tangent=1 point
f(x) -
= 3(x) (x) +
Determine:a ) AGbetween (1-2) and (0,0) b) AGbetween ec=-3 and x 4 =
AG= 0 2 +
(- 5; -
50)(4; 44) -
0 -
1
AG:
2
Y5c
--
↳ve=o n decreasing side parabola
of
44 30+
=
-
4 5
+
=-
2
c) AGbetween (2; f(z) and (3;f(3)
(2; -10) (3; -24)
AG y2 -y)
=
32 -31
24 10 +
=-
3-2
=
14
-
=
St di AG between (c;fle)) and locth;f(ecth))
↳
can'tfindnumerical values:
use
directly as points
AG yz y)
= -
32 -
6C1
f(x h) + - f(x) ->
firstprinciple
-
↳
finds the formula
H
general on
any graph
3(x h)2 (x h) ) -
3x2 x) ↳
fill in actual graphs
+ - +
+
- +
-
R
3(x2 zech n2) (x h) 3x2 -
x
-
aim is to cancel outh in denominator
-
+ + +
+ +
-
h
=-C2-beck-shth32
H
-
back -
k -
342
=>
H
k) -
bx -
1 -
3h)
=>
k
=- 66-5-1) general
formula ofaverage gradient
usedin a hence question to sub in
I
x= first (smallestgiven so values
h distancebtwec-values:(x2 -x.)
=
