Question

Mark all the relative minimum points in the graph.
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{7}\]
\[\small{\llap{-}2}\]
\[\small{\llap{-}3}\]
\[\small{\llap{-}4}\]
\[\small{\llap{-}5}\]
\[\small{\llap{-}6}\]
\[\small{\llap{-}7}\]
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{6}\]
\[\small{7}\]
\[\small{\llap{-}2}\]
\[\small{\llap{-}3}\]
\[\small{\llap{-}4}\]
\[\small{\llap{-}5}\]
\[\small{\llap{-}6}\]
\[\small{\llap{-}7}\]
\[y\]
\[x\]

Answer 1

I don't see the graph image — only the axis labels. Could you either upload the graph or describe it (coordinates of notable points, where the curve goes up/down, any open or closed dots)?

While you get that to me, here is how to find and mark all relative minima so you can do it or tell me the locations:

- A relative (local) minimum is a point on the graph where, in some small interval around the point, the function value is less than or equal to the values of nearby points. Visually it's a “valley.”
- On a smooth curve, these occur where the graph changes from decreasing to increasing (derivative changes from negative to positive).
- At endpoints of the domain, mark an endpoint as a relative minimum only if its value is less than nearby interior values.
- If the graph has a flat bottom (a horizontal segment), every point on that flat segment is a relative minimum; sometimes you mark the whole segment.
- Pay attention to open vs closed dots: a closed dot at the valley counts as a minimum, an open dot does not (unless the open dot is a limit point and the minimum is achieved elsewhere).

If you upload the graph or tell me coordinates/where the curve rises and falls, I will mark the exact relative minima for you.