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Calculus/Equation of Normal Line To Curve

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Expert: Alon Mandes - 4/2/2009


Question
The equation of the normal line to the curve
y = (x^2 - 1)^(1/3) at the point where x = 3 is

a. y + 12x = 38
b. y - 4x = 10
c. y + 2x = 4
d. y + 2x = 8
e. y - 2x = -4

How do i go about solving this?

Answer
Our curve is y = (x^2 - 1)^(1/3) . Therefore ,
y'=(1/3)(x^2-1)^(-2/3)*(2x)=(2x/3)/(x^2-1)^(2/3).
y'(3)=2/8^(2/3)=2/4=0.5
The normal has slope of -1/y'(3) which is -1/0.2=-2 . So the answer will be C or D .
y(3)=8^(1/3)=2. The normal line passes through the point(3,2)
So, 2=-2*3+n -> n=8 . So the answer is D .

Alon.

Calculus

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Alon Mandes

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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".

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

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

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