Which of the following most accurately identifies the relative extrema in the graph?
(1 point)
Responses
There is a relative maximum at (4,0)
and a relative minimum at (3,1)
.
There is a relative maximum at left parenthesis 4 comma 0 right parenthesis and a relative minimum at left parenthesis 3 comma 1 right parenthesis .
There is a relative maximum at (1.5,0)
and (4,0)
and a relative minimum at about (3,1)
.
There is a relative maximum at left parenthesis 1.5 comma 0 right parenthesis and left parenthesis 4 comma 0 right parenthesis and a relative minimum at about left parenthesis 3 comma 1 right parenthesis .
There is a relative minimum at (4,0)
and a relative maximum at about (3,1)
.
There is a relative minimum at left parenthesis 4 comma 0 right parenthesis and a relative maximum at about left parenthesis 3 comma 1 right parenthesis .
There is a relative minimum at (1.5,0)
and (4,0)
and a relative maximum at about (3,1)
.
There is a relative maximum at (4,0) and a relative minimum at (3,1).
The correct answer is:
There is a relative maximum at (4,0) and a relative minimum at (3,1).
To identify the relative extrema in a graph, you need to look for points where the graph changes from increasing to decreasing (relative maximum) or from decreasing to increasing (relative minimum). This can be done by analyzing the slope of the graph at different points.
In this case, we are given four options to choose from. Let's evaluate each option to determine which one accurately identifies the relative extrema in the graph.
Option 1:
There is a relative maximum at (4,0) and a relative minimum at (3,1).
This option states that there is a relative maximum and minimum at specific points on the graph.
Option 2:
There is a relative maximum at (1.5,0) and (4,0) and a relative minimum at about (3,1).
This option indicates that there are multiple relative maxima and a relative minimum, with approximate coordinates.
Option 3:
There is a relative minimum at (4,0) and a relative maximum at about (3,1).
This option suggests a relative minimum at (4,0) and an approximate relative maximum.
Option 4:
There is a relative minimum at (1.5,0) and (4,0) and a relative maximum at about (3,1).
This option states multiple relative minima and an approximate relative maximum.
By analyzing the given options, Option 1 appears to be the most accurate. However, it is always recommended to verify by graphing the function or equation and examining the points of intersection.