Find the max&min of the following function :

subject to the constraint :

By the Lagrang Multipliers' method :

........(1)

.......(2)

.......(3)

(1) will be :

(2) will be :

(3) will be :

then ?!!

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- May 16th 2010, 12:01 PMMissMultivariable max&min
Find the max&min of the following function :

subject to the constraint :

By the Lagrang Multipliers' method :

........(1)

.......(2)

.......(3)

(1) will be :

(2) will be :

(3) will be :

then ?!! - May 16th 2010, 12:40 PM11rdc11
- May 16th 2010, 12:47 PMMiss
thanks !!

But why did you ignore solving for in :

?? - May 16th 2010, 01:29 PMGeneral
**By using the method of Lagrange, we will get:**

**... (1)**

**... (2)**

**... (3)**

**... (4)**

**By substituting (1) in (2), we will get the equation :**

**..**

**when x=0 ---> y=0 , substitute this in 4 --->**

**so the first two points are and**

**when ---> z=4 from (3) ---> y=x from (1) and (2)**

**So when we have y=x and z=4 , By substituting t****his in (4) :**

**which don't have any solutions**

**so when , we do not have any points.**

**when ---> y=-4x from (1) and z=-1 from (3)**

**by substituting this in (4) --->**

**when x=1 --> y=-4 ---> third point is (1,-4,-1)**

**when x=-1 ---> y=4 ---> fourth point is (-1,4,-1)**

**The points are : and**

**Find the value of the function at these point, biggest --> max, smallest --> min.** - May 16th 2010, 02:12 PM11rdc11