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 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 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 and no relative minimum.

Answer 1

To determine the relative maximum and minimum of the polynomial function \( h(x) \), we would typically use calculus, specifically finding the first and second derivatives of the function. However, since we don't have the explicit form of the function \( h(x) \) provided here, I cannot perform the calculations.

Nevertheless, I can guide you on how to analyze the options provided:

1. Find the Critical Points: Set \( h'(x) = 0 \) to find the critical points.
2. Determine Nature of Critical Points: Use the first or second derivative test to determine whether each critical point corresponds to a relative maximum, minimum, or neither.
3. Identify the Values: Among the critical points identified, evaluate them to categorize as relative maxima or minima.

Since you have not provided the actual function or the derivatives, therefore, I'm unable to definitively evaluate the options given.

However, if you have performed the analysis or have the derivative information for \( h(x) \), you can select the option that corresponds with the critical points identified.

If you have specific values for derivatives or results of evaluations of \( h(x) \), please share them, and I can give a more targeted response.