This preview shows page 1. Sign up to view the full content.
MATH 23
Homework 7
due March 19, 2010
NonText Problems:
71.
Find the directional derivative of the function
f
(
x, y
) = sin(2
x

y
) at the
point
P
(

π
3
,
π
6
)
,
in the direction of the vector
±
v
=
<
π
3
,

π
6
>
. Also ﬁnd the
direction in which
f
increases most rapidly at
P
and the maximum rate of increase.
72.
Find equations for the tangent plane and the normal line to the surface
xy
+ 2
yz

xz
2
+ 10 = 0 at the point (

5
,
5
,
1)
.
73. Find the local maximum and minimum values and saddle points of the function
This is the end of the preview. Sign up
to
access the rest of the document.
Unformatted text preview: f ( x, y ) = x 24 xy + y 3 + 4 y. Show your work. 74. Use Lagrange multipliers to ﬁnd the maximum and minimum values of the function f ( x, y ) = xy subject to the constraint 9 x 2 + y 2 = 4 . Show your work. Text Problems to turn in: Friday, March 19: 14.6: 6, 16, 21; 14.7: 6, 10, 11; 14.8: 3, 4; 15.1: 4a. Text assignments for the remainder of the semester (main and complete) will be available shortly....
View
Full
Document
This note was uploaded on 03/26/2010 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .
 Spring '06
 YUKICH
 Calculus, Derivative

Click to edit the document details