help with maximum

[Ilovemymom]

If I want to find the Maximum of f(x) = x + 3/ (over is what I mean) x-3; [-4, 4] what should I do. I think it is 0 or there isn't a max, but I am not sure, any ideas any one?

 

[stapel]

You have posted:

. . . . .f(x) = x + 3/x - 3

. . . . .\(\displaystyle \large{f(x)\, =\, x\,+\,\frac{3}{x}\,-\,3}\)

Is this what you mean? Or do you mean something more along the lines of:

. . . . .f(x) = (x + 3) / (x - 3)

. . . . .\(\displaystyle \large{f(x)\, =\,\frac{x\,+\,3}{x\,-\,3}}\)

To find the maximum, one would take the first derivative, find the critical points, and determine which, if any, were local max points. Then compare the functional values at these extrema with the values at the interval endpoints. Whichever value is the greatest is the maximum on the listed interval.

I think it is 0

Please reply showing all of your work and reasoning thus far.

Thank you.

Eliz.