Lecture 22:
Second-Derivative Test
Reading for this lecture
HPW, Chapter 13, Section 13.4 &13.5.
Homework for Tutorial in Week 9
Exercise 13.4, page 599, problem 1.
Given y = x 2 - 5x + 6.
dy = 2x - 5.
dx
dy = 0 when x = 2.5.
dx
x = 2.5 implies y = 6.25 -
Lecture 23:
Applied Maxima and Minima
Reading for this lecture
HPW, section 13.6.
Homework for Tutorial in Week 9
Exercise 13.6, pages 616-620, problem 3.
Let x be the length of fencing parallel to the stream.
Let y be the length of fencing on one of the
Lecture 10:
Matrix Inverses
Reading for this lecture
HPW Chapter 6, Section 6.6.
Homework for Tutorial in Week 5
Exercise 6.6 problem 21.
6x + 5y = 2
x + y = -3
6
in matrix form is
1
6
We have to find the inverse of
1
5 x 2
=
1 y 3
5
.
1
6
1
5
1
1
0
0
Lecture 13:
The Derivative
Reading for this lecture
HPW, Chapter 11, Section 11.1.
Homework for Tutorial in Week 5
Exercise 11.1, page 499-500, problem 1.
Given
f(x) = x3 + 3
P= (x1,y1) = (-2, -5)
Point Q = (x2,y2) moves through 6 positions towards point
Lecture 24:
Differentials
Reading for this lecture
HPW, Section 14.1.
Homework for Tutorial in Week 9
Exercise 14.1, pages 630-1, problem 1.
Given
Exercise 14.1, pages 630-1, problem 7.
Given p = ln(x 2 + 7)
dp = d [ln(x 2 + 7)]dx
dx
= 22x dx
x +7
Exercis
Lecture 28: Applications of Partial Derivatives
Reading for this lecture
HPW, Chapter 17, Section 17.2.
Homework for Tutorial in Week 11
Exercise 17.2, pages 758-760, problem 1.
Given c = 7 x + 0.3 y 2 + 2 y + 900
where c is total cos t
x is the quantity
Lecture 3:
Compounding and Discounting
Reading for this lecture
HPW, Chapter 5, Sections 5.1, 5.2.
Homework for Tutorial in Week 3
Exercise 5.1, page 212-213 problem 1.
S = P(1 + r)n
where
P = $6,000 is the original principal
n = 8 years
r = 0.08 per year
Lecture 33 (part 2 of tutorial questions):
Constrained Optimization (2)
Ex 17.7, pp. 783-784, problem 17.
a) First we find critical point(s) using the Lagrange multiplier
method. This was done in the previous tutorial. Re-iterating:
Find x ($ per month sp
Lecture 32:
Constrained Optimization
Reading for this lecture
HPW, Chapter 17, Section 17.7.
Homework for Tutorial in Week 12
Ex 17.7, pp. 783-784, problem 1.
Given f(x,y) = x2 + 4y2 + 6;
2x 8y = 20
(x0,y0) is a critical point of f(x,y) = x2 + 4y2 + 6 sub
Lecture 29:
Higher-Order Partial Derivatives
Reading for this lecture
HPW, Chapter 17, Section 17.4.
Homework for Tutorial in Week 12
Exercise 17.4, page 764-765, problem 1.
f ( x, y) = 6 xy 2
6 xy 2
f x ( x, y) =
x
= 6 y2
6 y2
f xy ( x, y) =
y x
(6 y
Lecture 31:
Maxima and Minima of Functions of Two Variables
Reading for this lecture
HPW, Chapter 17, Section 17.6.
Homework for Tutorial in Week 12
Exercise 17.6, pp. 775-777, problem 21.
P = f(L,K) = 2.18L2 0.02L3 + 1.97K2 0.03K3
is a production functio
Lecture 30:
Maxima and Minima of Functions of Two Variables
Reading for this lecture
HPW, Chapter 17, Section 17.6.
Homework for Tutorial in Week 12
Exercise 17.6, pp. 775-777, problem 1.
f(x,y) = x2 3y2 8x + 9y + 3xy
has critical points where the two fir
Lecture 16:
Product and Quotient Rules
Reading for this lecture
HPW, Chapter 11, Section 11.4.
Homework for Tutorial in Week 7
Exercise 11.4, page 525-526, problem 1.
f(x) = (4x + 1)(6x + 3)
f '( x) = (4 x +1) d (6 x + 3) + (6 x + 3) d (4 x +1)
dx
dx
= (4