Question
Carmen was asked to identify the relative extrema of the polynomial function h(x)
. Which of the following statements should she make?
(1 point)
Responses
There is an absolute minimum at x=0.5
and a relative minimum at x=2
.
There is an absolute minimum at x equals 0.5 and a relative minimum at x equals 2 .
There is an absolute minimum at x=0.5
.
There is an absolute minimum at x equals 0.5 .
There is a relative maximum at x=0.5
.
There is a relative maximum at x equals 0.5 .
There is an absolute maximum at x=0.5
.
. Which of the following statements should she make?
(1 point)
Responses
There is an absolute minimum at x=0.5
and a relative minimum at x=2
.
There is an absolute minimum at x equals 0.5 and a relative minimum at x equals 2 .
There is an absolute minimum at x=0.5
.
There is an absolute minimum at x equals 0.5 .
There is a relative maximum at x=0.5
.
There is a relative maximum at x equals 0.5 .
There is an absolute maximum at x=0.5
.
Answers
GPT-4o mini
To accurately determine the relative extrema of the polynomial function \( h(x) \), Carmen would need to examine the function's critical points, which can be done by finding the first derivative \( h'(x) \) and identifying where it equals zero or is undefined.
Since we don't have the specific function \( h(x) \), it is impossible to assess the exact locations of the extrema. However, if we assume that the information provided states that there is an absolute minimum at \( x = 0.5 \) and a relative minimum at \( x = 2 \), then the statement Carmen should correctly make is:
"There is an absolute minimum at \( x = 0.5 \) and a relative minimum at \( x = 2 \)."
If \( x = 0.5 \) qualifies as an absolute minimum and \( x = 2 \) qualifies as a relative minimum according to the function's behavior, this statement would be correct. If you have more information or a specific form of \( h(x) \), please provide it for a more accurate assessment.
Since we don't have the specific function \( h(x) \), it is impossible to assess the exact locations of the extrema. However, if we assume that the information provided states that there is an absolute minimum at \( x = 0.5 \) and a relative minimum at \( x = 2 \), then the statement Carmen should correctly make is:
"There is an absolute minimum at \( x = 0.5 \) and a relative minimum at \( x = 2 \)."
If \( x = 0.5 \) qualifies as an absolute minimum and \( x = 2 \) qualifies as a relative minimum according to the function's behavior, this statement would be correct. If you have more information or a specific form of \( h(x) \), please provide it for a more accurate assessment.