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Queensland University of Technology **We aren't endorsed by this school

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BUSINESS MISC

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Mathematics

Date

Nov 2, 2023

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Assignment 17 - class notes
Mathematics IA (The University of Adelaide)
Studocu is not sponsored or endorsed by any college or university
Assignment 17 - class notes
Mathematics IA (The University of Adelaide)
Downloaded by Alice Yu ([email protected])
lOMoARcPSD|32041740

Cambridge Senior Mathematcs for the Australian Curriculum/VCE
Chapter 17 Diferentaton and antdiferentaton:
Assignment
1
Consider a curve with equation
y
= 2
x
2
+
x
.
a
If
P
is the point (1, 3) and
Q
is the point ((1 +
h
), 2(1 +
h
)
2
+ (1 +
h
)). Find the gradient of
chord
PQ
.
b
Find the gradient of
PQ
when
h
= 0.1.
c
Find the gradient of the curve at
P
.
2
For the function
f
(
x
) = 2
x
2
, find
.
)
(
)
(
lim
0
h
x
f
h
x
f
h
3
Evaluate the following limits:
a
x
x
x
9
)
3
(
lim
2
0
b
h
h
h
h
h
2
3
0
2
lim
c
2
8
lim
3
2
x
x
x
4
Find the derivative of each of the following:
a
4
3
8
3
x
x
y
b
)
2
(
2
3
2
x
x
x
y
c
)
1
)(
3
2
(
x
x
y
d
)
(
3
3
4
x
x
x
x
y
e
x
x
x
x
y
2
3
5
2
f
x
x
x
y
3
2
6
2
3
g
7
1
7
2
4
x
x
y
h
x
x
y
2
3
2
5
Let
8
2
3
4
x
x
x
y
.
a
Find the average rate of change of
y
between
x
= 1 and
x
= 2.
b
Find the gradient of the curve at
x
= 2.
6
For the graph shown, sketch the graph of the gradient function.
1
© Evans, Lipson, Wallace 2016
Downloaded by Alice Yu ([email protected])
lOMoARcPSD|32041740

Cambridge Senior Mathematcs for the Australian Curriculum/VCE
Chapter 17 Diferentaton and antdiferentaton:
Assignment
7
If
18
3
2
x
x
y
find the interval(s) for which
.
0
dx
dy
8
The function
3
6
3
)
(
2
3
t
t
t
s
represents the displacement of a particle moving along a
straight line, where
t
is in seconds and
s
is in metres.
a
Find the
position
of the particle after 3 seconds.
b
Find the
velocity
of the particle at that time.
9
The curve with equation
y
=
ax
2
+
bx
has a gradient of 5 at the point (1, -2).
a
Find the values of
a
and
b
.
b
Find the coordinates of the point where the gradient is 0.
10
For the graph of
f
:
R
→
R
, find:
a
{
x
:
f
′(
x
) > 0}
b
{
x
:
f
′(
x
) < 0}
c
{
x
:
f
′(
x
) = 0}
11
Find the coordinates of the points on the curve
y
=
x
2
+ 5
x
+ 3 at which the tangent:
a
makes an angle of 45° with the positive direction of the
x
-axis
b
is parallel to the line
y
= 3
x
+ 4.
12
Consider the equation
y
=
x
(
x
2
- 9).
a
Find the gradient at the points at which the curve crosses the
x
-axis.
b
Find the coordinates of the point on the curve at which the gradient = 0.
2
© Evans, Lipson, Wallace 2016
Downloaded by Alice Yu ([email protected])
lOMoARcPSD|32041740

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