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Return to Foundations of Science Mathematics 2e Student Resources
Chapter 10 Multiple choice questions
Partial differentiation
Quiz Content
*
not completed
.
Which of the following is
not
true of
z
= f(
x
,
y
) ?
z
is a function of two variables,
x
and
y
.
correct
incorrect
The partial derivative (∂
z
/∂
x
)
_{y}
gives the rate of change of
z
with respect to
x
when
y
is kept constant.
correct
incorrect
∂
z
/∂
x
)
_{y}
= (∂
z
/∂
y
)
_{x}
correct
incorrect
The gradient of
z
is a 2-dimensional vector.
correct
incorrect
*
not completed
.
If the gradient of a function of three variables Ω = f(
x
,
y
,
z
) is 4
i
+ 3
k
, what is the
rate of change of Ω in the direction 2
i
+ 2
j
–
k
?
1
correct
incorrect
5/3
correct
incorrect
5
correct
incorrect
15
correct
incorrect
*
not completed
.
If
z
=
x
^{2}
y
^{3}
+ ln(
y
), what is (∂
y
/∂
x
)
_{z}
?
-2
xy
^{4}
/ (3
x
^{2}
y
^{3}
+ 1)
correct
incorrect
3
xy
^{3}
/ (2
x
^{2}
y
^{2}
+ 1)
correct
incorrect
2
x
^{2}
y
^{3}
/ (
x
^{2}
y
^{2}
+ 3)
correct
incorrect
-3
x
^{2}
y
^{3}
/ (
x
^{2}
y
^{2}
+ 2)
correct
incorrect
*
not completed
.
Which of the following is
not
true at a maximum point of
z
= f(
x
,
y
) ?
(∂
z
/∂
x
)
_{y}
= 0 and (∂
z
/∂
y
)
_{x}
= 0
correct
incorrect
(∂
^{2}
z
/∂
x
^{2}
) (∂
^{2}
z
/∂
y
^{2}
) > (∂
^{2}
z
/∂
x
∂
y
)
^{2}
correct
incorrect
∂
^{2}
z
/∂
x
^{2}
+ ∂
^{2}
z
/∂
y
^{2}
< 0
correct
incorrect
It is the point where
z
takes the largest value possible.
correct
incorrect
*
not completed
.
If (∂
^{2}
z
/∂
x
^{2}
) (∂
^{2}
z
/∂
y
^{2}
) = (∂
^{2}
z
/∂
x
∂
y
)
^{2}
at a stationary point, what is its nature?
Minimum.
correct
incorrect
Maximum.
correct
incorrect
Saddle point.
correct
incorrect
Not able to characterise the nature on the given information.
correct
incorrect
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