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Calculus/Min/Max problem
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Question
Find the maximum possible area of an isosceles triangle where the two equal sides are both 6 cm long?
Suppose that the isosceles triangle has :
2 isosceles sides : 6,6
base : 2x
height : h
According to Pythagoras h=√(36-x^2).
The area of the triangle A=2x*h/2=xh=x√(36-x^2).
To find max/min area we derive A & set it equals zero :
A'(x)=√(36-x^2)+(-2x)x/2√(36-x^2)=√(36-x^2)-x^2/√(36-x^2).
A'=0 -> √(36-x^2)=x^2/√(36-x^2) -> 36-x^2=x^2 -> x=3√2.
A=x√(36-x^2)=(3√2)*√(36-(3√2)^2)=3√2*√(36-18)=18 cm^2.
Alon.
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Answers by Expert:
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".
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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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