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Expert: Alon Mandes - 12/14/2008


Question
Given the curve x^2 - xy + y^2 = 9

a. Write a general expression for the slope of the curve
b. Find the coordinates of the points on the curve where
the tangents are vertical
C. At the point (0,3) find the rate of change in the slope
of the curve with respect to x

Any help would be greatly appreciated

Answer
The slope of the implicit curve is calculate as an implicit  derivative of the implicit function x^2 - xy + y^2 = 9.
d/dx { x^2 - xy + y^2 = 9 } = d/dx { 0 }
2x-y-xy'+2yy'=0 -> y'=(y-2x)/(2y-x).
The tangent line is vertical when the slope is ∞. That will happen
when 2y=x -> At every point (xo,2xo) that satisfy :
xo^2-xo*2xo-4xo^2=9 -> -5xo^2=9 !! no such point. Meaning there are
no vertical tangent lines.
y'(0,3)=(3-0)/(6-0)= ½

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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