Calculus/calc

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Expert: Alon Mandes - 2/10/2009


Question
consider the curve defined by y^4=y^2-x^2
verify that dy/dx= x/y-2y63
write the equation for any horizontal/vertical tangent lines of the curve.

thanks.

Answer
Let's derive both sides with respect to x, keeping always in mind
that :
1. dx/dx=1
2. dy/dx=y'
So,let's perform derivative operator on the curve equation :
d/dx { y^4=y^2-x^2 } We get :
d[y^4]/dx=d[y^2-x^2]/dx
(4y^3)y'=2yy'-2x
(4y^3)y'-2yy'=-2x
y'(4y^3-2y)=-2x
y'(2y^3-y)=-x
y'(y-2y^3)=x
y'=x/(y-2y^3)

y'=0 When x=0 & in this case y= ±1 is the horizontal tangent lines.
y'=∞ When y-2y³=0 -> y(1-2y²)=0, Solutions : y1=0 & y2= ±√(½) If
we plug these solution into the graph curve we get x=±√(½) & x=0
are the vertical tangent lines .

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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