Where is the Global Maximum and Minimum?

Question

(Calculator allowed)

Where does the global maximum and minimum of f(x) = 1/x on [0, 3] occur? Remember to explain in the most concise and precise way possible.

A) No global maximum, global minimum at x = 3

B) Global maximum at x = infinity, global minimum at x = 3

C) No global maximum, no global minimum

D) Global maximum at x = 0, no global minimum

Answer 1

A) No global max, global min = 1/3 when x=3

y=1/x is a rectangular hyperbola when graphed

at x=0 1/0 it's undefined, the global max could be called "infinity" but that's wrong for a couple reasons. Infinity is not a real number. It's "only" a surreal number, a limit that is approached but never reached. Plus 1/0 could be positive or negative infinity. at x=0, there's a discontinuity in the graph as it jumps from + to - infinity, so it's sort of doubly undefined