findMax reduce to sort Can I reduce the find max (or find min) problem to the sort problem? Because if so, knowing the lower bound for find max is Ω(n) I can also infer that the lower bound for sorting is Ω(n) too?

I'm confused with this spread of lower bounds and applicability of reductions.
After you sort an array, the minimum can be found in the first position, and the maximum can be found in the last position. This reduces finding the minimum and maximum to sorting an array. However, sorting is actually more difficult than just finding the minimum or maximum, so it's not clear what this reduction is good for.