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Calculus/Equation of tangent line

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Expert: Alon Mandes - 11/7/2008


Question
Find the equation of the tangent line to the graph f(x)= (x^3+2x-4)(2x^2-(6/x)) at x=2.

Looking forward to your response.  thank you very much for your effort and help.

Answer
The tangent line is a strait line from the form : y=ax+b. So we
need to calculate a & b. 1st let's start with a :
a=f'(x) at x=2. Let's calculate f'(x) :
f'(x)=(x^3+2x-4)'(2x^2-6/x)+(x^3+2x-4)(2x^2-6/x)'
f'(x)=(3x^2+2)(2x^2-6/x)+(x^3+2x-4)(4x+6/x^2)
f'(2)=(3*4+2)(2*4-6/2)+(8+4-4)(8+6/4)
f'(2)=14*5+8*19/4
f'(2)=108.
So, the tangent line is y=108x+b. Let's calculate b:
We know that this line passes throuth the point (2,f(2)), so let's
substitute 2 & f(2) instead of x & y to get b :
f(2)=108*2+b -> b=f(2)-216=(2^3+2*2-4)(2*2^2-6/2)-216
-> b=(8+4-4)(8-3)-216=-176.
Hence , the tangent line is : y=108x-176

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 .

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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.

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M.A in Mathematics & Bs.c in Electronics.

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