Carmen was asked to identify the relative extrema of the polynomial function h(x) . Which of the following statements should she make?

Question

(1 point)
Responses

There is an absolute minimum at x=0.5.
There is an absolute minimum at x equals 0.5 .

There is an absolute minimum at x=0.5 and a relative minimum at x=2.
There is an absolute minimum at x equals 0.5 and a relative minimum at x equals 2 .

There is a relative maximum at x=0.5.
There is a relative maximum at x equals 0.5 .

There is an absolute maximum at x=0.5.

Answer 1

To determine which statement Carmen should make regarding the relative extrema of the polynomial function h(x), we need information about the behavior of the function at specific points.

Given the options provided, Carmen's response should include clear and precise language. The use of “at x=0.5” vs. “at x equals 0.5” is a stylistic choice, but both convey the same mathematical meaning.

If Carmen found that there is an absolute minimum at x=0.5 and a relative minimum at x=2, she should say:

"There is an absolute minimum at x equals 0.5 and a relative minimum at x equals 2."

If she only found one extreme, she would select the appropriate statement accordingly.

In summary, she should choose the statements that accurately reflect the results of her analysis on the polynomial function h(x).