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Calculus/Integration Calculus: Area

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Expert: Alon Mandes - 5/7/2010


Question
Area: Find the area of the largest rectangle that can be inscribed under the curve y=e^(-x^2) in the first and second quadrants.

The answer key showed how to start the question by doing:
A = (base)(height) = 2x(e^(-x^2))
I don't know how to finish thw question to the answer given of:
A = 2^(1/2)e^(-1/2) or square root 2 times e^(-1/2)

Answer
A(x)=2x[e^(-x^2)]
to find max , we derive with respect to x :
A'(x)=2[e^(-x^2)]+2x[-2xe^(-x^2)] . I simply followed the rule : [fg]'=f'g+fg' .
Thus,
A'(x)=2e^(-x^2)-(4x^2)e^(-x^2)
Now we must solve the equation A'(x)=0 :
2e^(-x^2)-(4x^2)e^(-x^2)=0
2e^(-x^2)=(4x^2)e^(-x^2)
1=2x^2
x=1/√2 .

A(1/√2)=[2/√2][ e^ ( -(1/√2)² ) ]=√2e^(-0.5)

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.

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

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