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Stewart_Calc_7ET ch14sec06
MULTIPLE CHOICE
1. Find the directional derivative of at the point (1, 3) in the direction
toward the point (3, 1).
Select the correct answer.
a.
b.
c.
d.
28
e.
none of these
2. Find the equation of the normal line to the given surface at the specified point.
a.
b.
c.
d.
e.
3. Find the directional derivative of the function at the point in the
direction of the unit vector that makes the angle with the positive x-axis.
a.
b.
1
c.
d.
11
4. Find equations for the tangent plane and the normal line to the surface with equation
at the point
a.
,
b.
,
c.
,
d.
,
5. Find equations for the tangent plane and the normal line to the surface with equation
at the point
a.
,
b.
,
c.
,
d.
,
6. Suppose that over a certain region of space the electrical potential V is given by
.
Find the rate of change of the potential at in the direction of the vector
.
a.
b.
44
c.
–2.91
d.
20
e.
7. Find the gradient of the function .
a.
b.
c.
d.
e.
8. Find the maximum rate of change of at the point (2,1).
In what direction does it occur?
a.
b.
c.
d.
e.
none of these
9. If use the gradient vector to find the tangent line to the level
curve at the point .
a.
b.
c.
d.
e.
MULTIPLE RESPONSE
1. Which of the given points are the points on the hyperboloid where the
normal line is parallel to the line that joins the points and .
Select all that apply.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. Find the equation of the tangent plane to the given surface at the specified point.
2. Find the direction in which the function decreases fastest at the point
.
3. Evaluate the gradient of f at the point P.
4. Find the equation of the normal line to the given surface at the specified point.
5. Find the gradient of the function .
SHORT ANSWER
1. Find the gradient of at the point
