Carmen was asked to identify the relative extrema of the polynomial function h(x) . Which of the following statements should she make?
(1 point)
Responses
There is an absolute maximum at x=0.5.
There is an absolute maximum at x equals 0.5 .
There is a relative maximum at x=0.5.
There is a relative maximum 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 an absolute minimum at x=0.5.
There is an absolute minimum at x equals 0.5 .
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Carmen should make the statement: "There is a relative maximum at x=0.5."
Carmen should make the following statement: "There is a relative maximum at x=0.5."
To identify the relative extrema of the polynomial function h(x), Carmen needs to analyze the critical points.
The relative extrema occur at the critical points where the derivative of the function is equal to zero or does not exist. Carmen should find the derivative of h(x) and set it equal to zero to solve for the critical points.
Once Carmen has identified the critical points, she can determine whether they are relative maxima or minima by examining the behavior of the function around those points. If the function changes from increasing to decreasing, the critical point is a relative maximum. If the function changes from decreasing to increasing, the critical point is a relative minimum.
Carmen should make the statement that there is a relative maximum at x=0.5.