Calculus/Calc

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Expert: Alon Mandes - 3/10/2010


Question
Use implicit differentiation to find the slope of the tangent line to the curve at the point (−4−1).

−4x2−4xy+4y3=−84

Answer
Hello Rebecca ,
The slope of the tangent line is defined as m=y' at point (-4,1) . to derive our implicit
curve, we follow the rule : d/dx {−4x²−4xy+4y³}= d/dx {−84} . we must keep in mind that
d/dx {x} =1  AND d/dx {y}=y' . For example : d/dx {y²} = 2yy' .
Hence,
d/dx {−4x²−4xy+4y³}= d/dx {−84}
- d/dx {4x²} − d/dx {4xy} + d/dx {4y³}= 0
-  8x        - (4y+4xy')  + 12y²y'    = 0
y'(12y²-4x)=8x+4y
y'=(2x+y)/(3y²-x)
m=y'{at -4,-1}=(-8-1)/(3+4)=-9/7

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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