What would be the graph of a function with two local maxima, a local minimum and without global minimums?
2026-04-08 22:46:35.1775688395
Graph of a function with two local maxima, a local minimum and without global minimums.
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Just draw it . . .
Two mountain tops and a valley between, then extend the outer parts down to minus infinity.
As an example, the following piecewise function satisfies the conditions . . . $$ f(x) = \begin{cases} 2+x&\text{if}\;\,x < -1\\[4pt] |x|&\text{if}\;\,-1 \le x \le 1\\[4pt] 2-x&\text{if}\;\,x > 1\\[4pt] \end{cases} $$ For another example, since there was no specified requirement for continuity, the following piecewise function satisfies the conditions, and moreover, has no global minimum and no global maximum . . . $$ g(x) = \begin{cases} 2+x&\text{if}\;\,x < -1\\[4pt] |x|&\text{if}\;\,-1 \le x \le 1\\[4pt] 2-x&\text{if}\;\,1 < x < 2\\[4pt] x-1&\text{if}\;\,x \ge 2 \end{cases} $$