HW4, Due date: October 17 (Monday)
1. Let .
a) At the point with x = 1 and y = 1, compute the unit vector
pointing in the direction of greatest increase of the function f(x, y)
and compute the rate of
Theorem 1. First derivative test for local extreme values.
If f x, y has a local maxium or minmum value at an interior point a, b of its
domain and if the first partial derivatives exist there, then f
: the rate of change of z at x0, y0 in the direction of an arbitrary
= < , >.
Math162 Calculus II
Korea University
Math162 Calculus II
Korea University
,
=< , >
Special cases:
if = =< 1,0 >, then
Arithmetic and Geometric progressions
A.P. Sn = a + (a + d) + (a + 2d) +
+ [a + (n 1)d] =
n
2
[2a + (n 1)d]
G.P. Sn = a + ar + ar2 +
+ arn1 = a
1 rn
1r
,
S1 =
a
1r
for jrj < 1
(These results also hold