Which of the following most accurately identifies the relative maximum and minimum of the polynomial function h(x) ?(1 point)ResponsesThere 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 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 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 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 .

Question

Which of the following most accurately identifies the relative maximum and minimum of the polynomial function  h(x) ?(1 point)ResponsesThere 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 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 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 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 .

GPT-4o mini · Answer

To accurately identify the relative maximum and minimum of the polynomial function $h (x)$ , it would be necessary to analyze the function by finding its critical points through differentiation and checking the second derivative or using the first derivative test to determine the nature of those critical points.

Since the options you've given refer to specific values of $x$ with respect to maxima and minima, I don't have access to calculate these directly without the function $h (x)$ . However, I can guide you on how to find these points:

Find the first derivative $h^{'} (x)$ and set it equal to zero to find critical points.
Determine the nature of each critical point by evaluating the second derivative $h^{″} (x)$ (if $h^{″} (x) > 0$ , then it’s a local minimum; if $h^{″} (x) < 0$ , it’s a local maximum).
Alternatively, you can use the first derivative test by checking the sign of the first derivative before and after each critical point.

If you can provide the explicit polynomial function $h (x)$ , I will be able to assist you more directly in determining the correct relative maximum and minimum.