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About 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.

You are here: Experts > Teens > Homework/Study Tips > Calculus > Unknown values

Calculus - Unknown values

Expert: Alon Mandes - 11/5/2009

Question
I'm not sure how to approach this problem.

For what values of the numbers A and B does the function f(x)= Axe^(Bx^2) have the the maximum value f(2)=1?

Thanks in advance.

Answer
It's given that f(2)=1. Therefore : A(2)e^(B(2)^2)=1 --> 2Ae^(4B)=1 --> A=1/[2e^(4B)] -->
A=(1/2)e^(-4B) .
We also know that at x=2 there is maximum. So, we derive the function & substitute x=2 & set
the equation equal zero :
f'(x)=Ae^(Bx^2)+2ABxe^(Bx^2) . f'(2)=Ae^(4B)+4ABxe^(B4) . f'(2)=0 --> Ae^(4B)+4ABe^(B4)=0 -->
A+4AB=0 --> (1+4B)=0 --> B=-1/4 .
A=(1/2)e^(-4B) --> A=(1/2)e^(-4[-1/4])=e/2 .

Alon.

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