Question

How many points on the graph represent a relative minimum? please help

Answer 1

Answer:  1

Point B is the only relative minimum here.

===========================================================

Explanation:

A relative minimum is a valley point, or lowest point, in a given neighborhood. Points to the left and right of the valley point must be larger than the relative min (or else you'd have some other lower point to negate its relative min-ness).

Point B is the only point that fits the description mentioned in the first paragraph. For a certain neighborhood, B is the lowest valley point so that's why we have a relative min here.

There's only 1 such valley point in this graph.

--------------

Side notes:

• Points A and D are relative maximums since they are the highest point in their respective regions. They represent the highest peaks of their corresponding mountains.
• Points A, C and E are x intercepts or roots. This is where the graph either touches the x axis or crosses the x axis.
• The phrasing "a certain neighborhood" is admittedly vague. It depends on further context of the problem. There are multiple ways to set up a region or interval of points to consider. Though visually you can probably spot a relative min fairly quickly by just looking at the valley points.
• If you have a possible relative min, look directly to the left and right of this point. if you can find a lower point, then the candidate point is not a relative min.