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Calculus/minima problem

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Expert: Alon Mandes - 6/8/2009


Question
sir,
 how can i find minima of z=f(x,y). that for what values of x and y, z will b minimum.

Answer
1st you need to calculate these forms :
1. ∂z/∂x
2. ∂z/∂y
3. ∂²z/∂x²
4. ∂²z/∂y²
5. ∂²z/∂x∂y
Now, you need to solve : ∂z/∂x=0 & ∂z/∂y=0. The solution will give
you the critical points of the function z, let's say the point is
(a,b).
Now you have to calculate the form :
D(x,y)=[∂²z/∂x²]*[∂²z/∂y²]-[∂²z/∂x∂y]².
If D(a,b)<0 then (a,b) is a saddle point.
If D(a,b)>0 then point (a,b) is a local maxima or minima depends on:
1. If ∂²z/∂x²(a,b) > 0 then (a,b) mimina
2. If ∂²z/∂x²(a,b) < 0 then (a,b) maxima

Alon.

Calculus

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Alon Mandes

Expertise

Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .

Experience

1. I'm a team member of mathnerds (math site for answering questions) 2. I'm a team member in the Student's Union of the Technion, helping students who have problems in mathematics. 3. 2 years of experience as a math teacher in college. 4. I give free homework help for high school students in Mathematics & Physics. 5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" , "Complex Functions".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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