# Obtaining the maximum of a shifted function

• Jun 19th 2010, 06:14 AM
Anindya
Obtaining the maximum of a shifted function
I have a continuous function f(x) , whose maximum Fm occuring at x=Xo is known.

Can we find the maximum of g(x) = f(x+A) + f(x-A) from the above information and the value of x where we have the maximum of g(x) ?

Is there any way to do this please let me know.

Thanks & Regards
Anindya
• Jun 19th 2010, 06:16 AM
Ackbeet
Is f differentiable? Over what interval are you maximizing the function? Does the maximum of f that you know occur at a critical point, or at an endpoint of your interval of interest?
• Jun 19th 2010, 06:19 AM
Anindya
Yes F is differentiable . Sorry i forgot to add that. The maximum of f occurs at a critical point
• Jun 19th 2010, 06:21 AM
SpringFan25
except in trivial cases (eg A=0), i dont think you can do this from the information provided. Do you have any more information about f(x)
• Jun 19th 2010, 06:24 AM
Anindya
No i don't.
• Jun 19th 2010, 06:27 AM
Ackbeet
Ok, f differentiable implies g is differentiable. The derivative of g is

\$\displaystyle g'(x)=f'(x+A)+f'(x-A)\$.

As SpringFan25 has noted, setting \$\displaystyle g'(x)=0\$ is a bit problematic. I'm not exactly sure how you would go about solving that. You know that \$\displaystyle f'(x_{0})=0\$. But I'm not seeing where you would go next. For, if you set \$\displaystyle x+A=x_{0}\$, then \$\displaystyle x=x_{0}-A\$, and \$\displaystyle x-A=x_{0}-2A\$. Then what? You don't know that the second term is zero.
• Jun 19th 2010, 09:39 AM
p0oint
Use the definition of derivative... Just and idea...
• Jun 19th 2010, 11:42 AM
mfetch22
Quote:

Originally Posted by Anindya
I have a continuous function f(x) , whose maximum Fm occuring at x=Xo is known.

Can we find the maximum of g(x) = f(x+A) + f(x-A) from the above information and the value of x where we have the maximum of g(x) ?

Is there any way to do this please let me know.

Thanks & Regards
Anindya

I know that the maximum of the function f(x+A) is x=Xo-A, and that the maximum of the function f(x-A) is x=Xo+A, but I'm not sure how to do it when the functions are added together. I'm not sure where to go on this one, like the previous poster said, is there anymore information about f(x)? I hope the facts above about the sperate functions help, otherwise I've just wasted space.