Question
The graph of a fourth degree polynomial function is shown.The function begins in quadrant 2, decreases to the point left-parenthesis negative 2 comma negative 9.67 right-parenthesis, increases to the point left-parenthesis 1 comma 6.08 right-parenthesis, decreases to the point left-parenthesis 3 comma 0.75 right-parenthesis, and increases as it continues to the right.
Question
Use the graph to answer the question.
Determine which statements are true about the extrema of the graphed fourth degree polynomial. Select all that apply.
(1 point)
Responses
left parenthesis negative 2 comma negative 9.67 right parenthesis and left parenthesis 3 comma 0.75 right parenthesis are global minima for the function.
Image with alt text: left parenthesis negative 2 comma negative 9.67 right parenthesis and Image with alt text: left parenthesis 3 comma 0.75 right parenthesis are global minima for the function.
left parenthesis 1 comma 6.08 right parenthesis is the global maximum for the function.
Image with alt text: left parenthesis 1 comma 6.08 right parenthesis is the global maximum for the function.
left parenthesis 1 comma 6.08 right parenthesis and left parenthesis 3 comma 0.75 right parenthesis are local extrema for the function.
Image with alt text: left parenthesis 1 comma 6.08 right parenthesis and Image with alt text: left parenthesis 3 comma 0.75 right parenthesis are local extrema for the function.
left parenthesis negative 2 comma negative 9.67 right parenthesis is the global minimum for the function.
Question
Use the graph to answer the question.
Determine which statements are true about the extrema of the graphed fourth degree polynomial. Select all that apply.
(1 point)
Responses
left parenthesis negative 2 comma negative 9.67 right parenthesis and left parenthesis 3 comma 0.75 right parenthesis are global minima for the function.
Image with alt text: left parenthesis negative 2 comma negative 9.67 right parenthesis and Image with alt text: left parenthesis 3 comma 0.75 right parenthesis are global minima for the function.
left parenthesis 1 comma 6.08 right parenthesis is the global maximum for the function.
Image with alt text: left parenthesis 1 comma 6.08 right parenthesis is the global maximum for the function.
left parenthesis 1 comma 6.08 right parenthesis and left parenthesis 3 comma 0.75 right parenthesis are local extrema for the function.
Image with alt text: left parenthesis 1 comma 6.08 right parenthesis and Image with alt text: left parenthesis 3 comma 0.75 right parenthesis are local extrema for the function.
left parenthesis negative 2 comma negative 9.67 right parenthesis is the global minimum for the function.
Answers
GPT-4o mini
To analyze the statements about the extrema of the given fourth degree polynomial based on the provided graph, let's evaluate each statement:
1. **(−2, −9.67) and (3, 0.75) are global minima for the function.**
- Incorrect: (−2, −9.67) is a local minimum, but (3, 0.75) is not a minimum; it’s a point of increase.
2. **(1, 6.08) is the global maximum for the function.**
- Correct: Since the graph reaches a peak at (1, 6.08) before decreasing again, this point is likely the global maximum.
3. **(1, 6.08) and (3, 0.75) are local extrema for the function.**
- Correct: (1, 6.08) is a local maximum (because it is a peak), and (3, 0.75) is a local minimum (since the function decreases to (3, 0.75) and then increases afterwards).
4. **(−2, −9.67) is the global minimum for the function.**
- Incorrect: (−2, −9.67) is a local minimum, but it is not the global minimum because the function decreases to this point and increases afterwards.
Based on this analysis, the true statements are:
- **(1, 6.08) is the global maximum for the function.**
- **(1, 6.08) and (3, 0.75) are local extrema for the function.**
1. **(−2, −9.67) and (3, 0.75) are global minima for the function.**
- Incorrect: (−2, −9.67) is a local minimum, but (3, 0.75) is not a minimum; it’s a point of increase.
2. **(1, 6.08) is the global maximum for the function.**
- Correct: Since the graph reaches a peak at (1, 6.08) before decreasing again, this point is likely the global maximum.
3. **(1, 6.08) and (3, 0.75) are local extrema for the function.**
- Correct: (1, 6.08) is a local maximum (because it is a peak), and (3, 0.75) is a local minimum (since the function decreases to (3, 0.75) and then increases afterwards).
4. **(−2, −9.67) is the global minimum for the function.**
- Incorrect: (−2, −9.67) is a local minimum, but it is not the global minimum because the function decreases to this point and increases afterwards.
Based on this analysis, the true statements are:
- **(1, 6.08) is the global maximum for the function.**
- **(1, 6.08) and (3, 0.75) are local extrema for the function.**