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Expert: Alon Mandes - 11/2/2008


Question
Trying to find   2nd derivative   of  4x^2  +  y^3   = 2x  + 7y   at (-1, 2)



1st  derivative   gives  ans  = 2   as book

2nd                 gives  -8/5    book gives  -56/5      Confussed



Any help appreciated   Cassie  

Answer
Let's derive with respect to x :

d/dx { 4x^2+y^3=2x+ 7y } = 8x+3y^2*y'=2+7y' -> y'(7-3y^2)=8x-2 ->
y'=(8x-2)/(7-3y^2) . y'(-1,2)=(-8-2)/(7-12) =2 .

d/dx { 8x+3y^2*y'=2+7y' } = 8+3y^2*y''+6yy'=7y''
-> y''(3y^2-7)=-8-6yy' -> y''=(8+6yy')/(7-3y^2)
-> y''(-1,2)=(8+6*2*2)/(7-3*4)=-32/5.
You can conferm that by deriving (8x-2)/(7-3y^2) & subtitute (-1,2)
you will get the same result -32/5. & it's correct !


Alon.

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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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