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You should derivate f(x). Then equal that derivative to zero and solve for x. If you have problem with derivation, let me know, please.
I got f'(x)=-(X^2+2x-8)/(x^2+8)^2 the continuous roots are x=-4, 2, discontinuity at x=+2(2)^(1/2),x=-2(2)^(1/2), so you don't count them. The relative max is x=2, is this right?
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