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?
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
Ok, f differentiable implies g is differentiable. The derivative of g is
.
As SpringFan25 has noted, setting is a bit problematic. I'm not exactly sure how you would go about solving that. You know that . But I'm not seeing where you would go next. For, if you set , then , and . Then what? You don't know that the second term is zero.
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.