School of Mathematics and Statistics
Carleton University
Math. 69.204B
ANSWERS TO TEST 3
Reason:
, which is (4,1,-2) at P.
Reason: With x=t and , we have
and
. Hence
Reason: The gradient vector of at
P=(1,1, 2) is
which is normal to S at P. On the other hand,
is normal to the plane
. So
the vector
is tangent to
the curve at P.
Reason: By the chain rule, we have
Answer. The condition yields
giving , x=-1, y=-4/2=-2 and
. Thus the minimum
value of f subject to g=0 is
.
Answer. Setting and
, we have
solving this linear system, we have x=-1, y=2, which gives us a critical point (-1, 2). At this point
Hence (-1, 2) is a saddle point.