Lecture6bc - Welcome to Math 122 Lecture 6 Survey of...

Instructor: Quanlei Fang
Dept. of Math, University at Buffalo, Spring 2009
Welcome to
Math 122 Lecture 6
Survey of Calculus and its Applications I1
Partial derivatives
Last time
Last time
Definition Example
Partial Derivative of f ( x , y )
with respect to x : written ,
the derivative of f ( x , y ),
where y is treated as a
constant and f ( x , y ) is
considered as a function of x
alone
If , then
x
f
∂
∂
( )
4 3 2 , y x y x f =
. 8
and 6
3 3
4 2
y x
y
f
y x
x
f
=
∂
∂
=
∂
∂

Maxima and Minima of Functions
Maxima and Minima of Functions
of Several Variables
of Several Variables
§ 7.3
Relative Maxima and Minima
First Derivative Test for Functions of Two Variables
Second Derivative Test for Functions of Two
Variables
Finding Relative Maxima and Minima
Relative Maxima & Minima
Relative Maxima & Minima
Definition Example
Relative Maximum of f ( x , y ):
f ( x , y ) has a relative
maximum when x = a , y = b
if f ( x , y ) is at most equal to
f ( a , b ) whenever x is near a
and y is is near b .