Quiz 9: Maxima and minima of functions of two variables
Question 1
Find the critical point and its nature for the function
.
when x = 1.
when y = -1.f = -5 at (1,-1).
The surface is concave up at all points.
Question 2
The function
has one critical point. Determine its
position and nature.
when x = 1.
when y = 2.f = 10 at (1,2).
The surface is concave down at all points.
Question 3
How many critical points has the function
?

Question 4
Find the horizontal tangent plane to the surface
when
x = 1.

.Question 5
Which equation most closely corresponds to the sketch of the surface below ?

Question 6
What does
mean ?
![]() | (1) |
Question 7
Which of the following represents 2 + 7 + 14 + 23 + 34 in summation notation ?
![]() | (2) |
Question 8
An airline will only accept luggage whose “linear length” height + width + length is at most 200cm. Assume that you will choose a suitcase with a standard box shape. Which of the following correctly represents the problem of finding what is the maximum volume that your suitcase can be?
Question 9
An airline will only accept luggage whose “linear length” height + width +
length is at most 200cm. Assume that you will choose a suitcase with a
standard box shape. What is the maximum volume that your suitcase can
be?
Hint: The solution to 200x - y2 - 2xy = 0 and 200y - x2 - 2xy = 0, x,y ≥ 0 is
x = y =
Question 10
An airline will only accept luggage whose “linear length” height + width + length is at most 200cm. Assume that these are measured at the widest part of the piece of luggage. Could you carry more using a spherical suitcase than using a box-shaped suitcase as described in questions 8 and 9?
cm will have volume (
)3cm3 = 296,000cm3
approximately.
A sphere with the same diameter would have radius
cm, so its volume would be
(
)3 = 155,140cm3 approximately.
right first
right
wrong
