Which of the following most accurately identifies the relative maximum and minimum of the polynomial function h(x)?

Question

(1 point)
Responses

There is a relative maximum at x=−1 and a relative minimum at x=0.555.
There is a relative maximum at x equals negative 1 and a relative minimum at x equals 0.555 .

There is a relative maximum at x=−1 and no relative minimum.
There is a relative maximum at x equals negative 1 and no relative minimum.

There is a relative minimum at x=−1 and a relative maximum at x=0.555.
There is a relative minimum at x equals negative 1 and a relative maximum at x equals 0.555 .

There is a relative maximum at x=1.5 and a relative minimum at x=−2.

Answer 1

To accurately identify the relative maximum and minimum of the polynomial function \( h(x) \), you would typically need to analyze the first and second derivatives to find critical points and determine their nature. However, since the function itself has not been provided, I can't perform an analysis on it.

If the possible responses are based on your own analysis or on known properties of \( h(x) \), please refer to the computed critical points and their values.

To summarize the responses given:

1. Relative maximum at \( x = -1 \) and relative minimum at \( x = 0.555 \).
2. Relative maximum at \( x = -1 \) and no relative minimum.
3. Relative minimum at \( x = -1 \) and relative maximum at \( x = 0.555 \).
4. Relative maximum at \( x = 1.5 \) and relative minimum at \( x = -2 \).

Without additional information about \( h(x) \) or its derivatives, I cannot definitively conclude which response is correct. Please check your calculations or provide the details of the function for further assistance.