Assignment Booklet 08
4
Exponential and Logarithmic Functions
0.01t
3. The number of bacteria y after time t (in minutes) is given by y = 10 000e
. At what rate
is the population changing at t = 3 minutes? Express your answer to the nearest unit. Is th

Assignment Booklet 06
5
Applications of the Derivative
7. A fish is being reeled in at a rate of 30 cm/s from a bridge 4 m
above water. At what rate is the angle (in rad/s) between the
line and the water changing when there is 8 m of line out?
ADLC Mat

Applications of the Derivative
6
4
6
Assignment Booklet 06
2. You hit a golfball vertically upward with your pitching wedge. The position function of
3t 2 + 30t where the origin is at ground level and the positive direction is
the ball is s (t ) =
vert

Assignment Booklet 06
Applications of the Derivative
150 s
4
4. The relation between distance s and velocity v is given by v =
. Find the acceleration
3+ s
in terms of s.
3
5. A pebble is dropped into a still pond, causing ripples in the form of conce

Applications of the Derivative
Assignment Booklet 06
Section 2 Assignment: Rates of Change
Read all parts of your assignment carefully and record your answers in the appropriate
places.
1. An object is moving in a straight line from a fixed point. The d

Assignment Booklet 06
Applications of the Derivative
4
3. Two straight highways are perpendicular to each other. Car A is 3 km from the intersection
and is moving at 100 km/h toward the junction. On the other highway, Car B is 5 km from
the intersectio

Assignment Booklet 06
Applications of the Derivative
5
5. Two isolated farms are situated 12 km apart on a straight country road that runs parallel to
the main highway 20 km away. The power company decides to run a wire from the highway
to the junction

Applications of the Derivative
Assignment Booklet 06
Section 3 Assignment: Related Rates
Read all parts of your assignment carefully and record your answers in the appropriate
places.
4
1. The height h of an equilateral triangle is increasing at a rate

Applications of the Derivative
5
5
2
Assignment Booklet 06
2. A can of peanuts has a circular base and top, and it is cylindrical in shape. The volume is
500 cm3. If the can is to require the least amount of material, what must its dimensions be?
Give

Assignment Booklet 06
Applications of the Derivative
Assignment Booklet
Mathematics 31 Module 6:
Applications of the Derivative
105
Your mark on this module will be determined by how well you do your assignments in this
booklet.
Work slowly and carefull

Assignment Booklet 05
Curve Sketching
Final Module Assignment
Read all the parts of your assignment carefully and record your answers in the appropriate
place.
6
1. Use the first and second derivatives of the function y = x 3 3 x 2 9 x + 15 to find the

Curve Sketching
Assignment Booklet 05
4
3. Determine the point of inflection, if it exists, on the graph of =
y x 4 4 x3 .
3
4. Determine where the curve y = x 3 + 4 x 2 2 x + 1 is concave up and concave down.
4
5. Find any points of inflection for th

Assignment Booklet 05
Curve Sketching
f. Determine the maximum and minimum values.
2
1
g. Where is the curve concave upward or downward?
1
2
i. Sketch the graph of the function.
h. Locate the points of inflection (if any).
f (x)
4
3
2
1
-4
-3

Curve Sketching
Assignment Booklet 05
Section 3 Assignment: The First Derivative
Read all the parts of your assignment carefully and record your answers in the appropriate
place.
1. Use the following partial graph of a polynomial function, with a local

Curve Sketching
Assignment Booklet 05
4
3. Determine the point of inflection, if it exists, on the graph of =
y x 4 4 x3 .
3
4. Determine where the curve y = x 3 + 4 x 2 2 x + 1 is concave up and concave down.
4
5. Find any points of inflection for th

Assignment Booklet 05
2
Curve Sketching
4. Express the domain and range of the following curve in interval notation.
y
4
(1, 3)
3
2
1
-2
-1
1
2
3
4
x
-1
-2
(3, 2)
-3
Section 2 Assignment: Asymptotes
Read all the parts of your assignment carefully and r

Assignment Booklet 05
4
Curve Sketching
6. Use the second derivative test to find the maximum and minimum points of
f ( x) =2 x 3 + 15 x 2 36 x .
Section 5 Assignment: Curve-Sketching Procedures
Read all the parts of your assignment carefully and recor

Assignment Booklet 05
Curve Sketching
Section 4 Assignment: The Second Derivative
Read all the parts of your assignment carefully and record your answers in the appropriate
place.
3
( x) x 2 (1 x) is concave upward.
1. Using the second derivative, dete

Applications of the Derivative
5
12
Assignment Booklet 06
3. A solid is formed by attaching a hemisphere to each end of a cylinder. If the total volume
is to be 120 cm3, find the radius (in centimetres) of the cylinder that produces the minimum
surface

Applications of the Derivative
5
16
Assignment Booklet 06
8. You are in a sea kayak 400 m offshore from point A. You are along a straight sandy beach. A
storm is brewing and you wish to go to a shelter 1000 m down the beach from A. If you can
paddle yo

Assignment Booklet 06
Applications of the Derivative
Final Module Assignment
Read all parts of your assignment carefully and record your answers in the appropriate
places.
4
1. While you were out cross country skiing, you make a perfectly shaped spheri

Exponential and Logarithmic Functions
Assignment Booklet 08
4
2. The rate at which a radioactive isotope disintegrates is proportional to the amount present. If
a 30 g sample will contain only 20 g after ten minutes, what is the half-life of this isotop

Assignment Booklet 08
Exponential and Logarithmic Functions
Section 2 Assignment: Applications
Read all the parts of your assignment carefully and record your answers in the appropriate
place.
4
1. A population of grasshoppers quadruples in twenty days

Assignment Booklet 08
Exponential and Logarithmic Functions
1
d. lim ln( x 2)
3
17. What interest rate, compounded continuously, will triple the size of your account in five
years? Express your answer to the nearest percent.
1
18. Express log 7 13 i

Assignment Booklet 08
2
Exponential and Logarithmic Functions
x
12. What is the x-intercept of the tangent
=
to y e=
at x 45 ?
3
13. Differentiate y = xesin x .
3
14. What is the area bounded by y = (cos x)esin x and the x-axis, between x = 0 and x =

Assignment Booklet 08
Exponential and Logarithmic Functions
3
7. If ln 5 = a and ln 3 = b, write ln 0.12 as an expression in a and b.
2
8. Write y =
3
9. Determine the inverse =
of y 3ln( x 1) . Write your answer in the form y = f ( x) .
ADLC Mathemat

Assignment Booklet 08
Exponential and Logarithmic Functions
b. By applying the rules for natural logarithms, how could the answer in question 3.a. be
expressed so that the absolute value symbol is not required?
2
4
4. Integrate the following:
2
a.

Exponential and Logarithmic Functions
Assignment Booklet 08
2. Differentiate the following:
3
3
1
y ln(3 x 2) 2
a. =
b. y = x [ ln x ]
2
2
3. a. The antiderivative of f ( x) = is written as f ( x) = 2 ln | x | . Why must the absolute
x
value symbo

Assignment Booklet 08
Exponential and Logarithmic Functions
Assignment Booklet
MAthematics 31 Module 8: Exponential and
LogarithmiC Functions
90
Your mark on this module will be determined by how well you do your assignments in this
booklet.
Work slowly

Assignment Booklet 07
2
The Integral
4. Perform the definite integration.
6
2
( x + 1)
0
2
dx
dy
dx
2
5. Solve the differential equation = 3 x 4 + 5 x if y = 3 when x = 0.
2
x 2 2 x + 5 and y =
x 2 + 2 x 2 and the pair of
6. Find the area bound b