Question

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

(1 point)
Responses

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.
There is a relative maximum at x equals 1.5 and a relative minimum at x equals negative 2 .

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.

Answer 1

To accurately identify the relative maximum and minimum of the polynomial function \( h(x) \), you typically need to analyze the function. This usually involves finding the critical points by taking the derivative \( h'(x) \), setting it to zero, and solving for \( x \). Then, you would analyze the second derivative or use the first derivative test to determine whether each critical point is a maximum, minimum, or neither.

Since you provided multiple-choice answers without giving the polynomial function itself, I can’t determine which response accurately reflects the correct relative maximum and minimum of \( h(x) \).

However, if you have access to the polynomial function, you can analyze it as follows:

1. **Find the derivative**.
2. **Set the derivative equal to zero** to find critical points.
3. **Test those critical points** to determine whether they are maxima or minima.

If you share the actual polynomial function, I could help with further analysis or confirm which option would be correct based on that function.