The given graph has two absolute minima as no points are below them and one relative maximum as there is a change in direction from increasing to decreasing at that point. Hence, Option A. True is the right choice.
What are absolute maxima and absolute minima?
The absolute maxima and absolute minima are the points on the graph where the graph shows the highest and the lowest values respectively.
What are relative maxima and relative minima?
The relative maximum is the point on the graph where the graph changes its direction from an increasing function to a decreasing function.
The relative minimum is the point on the graph where the graph changes its direction from a decreasing function to an increasing function.
How to solve the question?
In the question, we are asked whether the given statement:
The function whose graph is shown below has the following characteristics.
• Two absolute minima
• One relative maximum,
is true or not.
In the given graph, we can observe that it was first a decreasing function, until a certain point, then it starts increasing until a certain point, then again decreased until a certain point, and after that went on increasing.
Hence it shows 3 points of inflections.
The first point is an absolute minimum point as the graph never goes below it.
The second point is a relative maximum as there is only a change in direction at that point, and there are points higher than that point.
The third point is an absolute minimum point as the graph never goes below it.
Therefore, we can say that the graph has:
- Two absolute minima
- One relative maximum
Hence, the given statement is A. True.
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