-
Find the directional derivative of
at the point in the direction
corresponding to the angle .
-
- Find the gradient of
,
- Evaluate the gradient at the point ,
- Find the rate of change of at in the direction
of the vector .
-
-
-
-
- Find the gradient of
,
- Evaluate the gradient at the point ,
- Find the rate of change of at in the direction
of the vector .
-
Find the directional derivative of the function
at the point
in the direction of the vector .
.
-
Find the maximum rate of change of
at the point
and the direction in which it occurs.
and .
-
Find the maximum rate of change of
at the point
and the direction in which it occurs.
, .
-
Find the directions in which the directional derivative
of
at the point
has the value .
and .
-
Find the equations of the tangent plane and the normal line
to the surface
at the point .
and
-
Find the equations of the tangent plane and the normal line
to the surface
at the point .
-
Let .
Find the gradient vector
and use it to find the tangent line to the level curve
at the point .
Sketch the level curve, the tangent line, and the gradient
vector.
and .
-
Find the points on the ellipsoid
where the tangent plane is parallel to the plane
.
.
-
Find parametric equations for the tangent line to the curve
of intersection of the paraboloid
and the ellipsoid
at the point .