General question about solving force maximization problems

Ceenaya19
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I'm doing this E&M problem for fun (I'll be taking the class this fall), but now it's just starting to get frustrating. I can't really post the problem because there is a diagram, but I'm not really looking to be given the actual solution anyway, so I'll describe it to you:

Two positive charges on the y-axis are acting on a single positive charge on the x-axis. The problem asks me to determine the x-position at which the single positive charge experiences the maximum force. I derived an expression to describe the superposition of the two positive electric forces on the single positive charge; then, to maximize it, I differentiated it, set it equal to zero, and solved for "x".

My answer does not match the answer in my textbook, but I can't think of any other way to do this problem; I always assumed that maximization was straightforward. So, could someone please point me in the right direction, conceptually? Thanks.
 
on Phys.org
Did you take the vector sum and maximize its magnitude, or did you ignore how each charge provides a force in a different direction?
 
Two on y axis, and one on x axis.
So, the position is on the x axis. Please thinking again.
 

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