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 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=1.5 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 no relative minimum.
There is a relative maximum at x equals negative 1 and no relative minimum.
There is a relative minimum at x=−1 and a relative maximum at x=0.555.
There is a relative minimum at x=−1 and a relative maximum at x=0.555.
The correct response is: "There is a relative maximum at x=−1 and a relative minimum at x=0.555."
To find the relative maximum and minimum of a polynomial function, one can use calculus. The first step is to take the derivative of the function and set it equal to zero. The solutions to this equation will give the critical points of the function.
In this case, we need to determine the critical points of the polynomial function h(x). Once we find these critical points, we can determine whether they correspond to relative maximums or minimums by analyzing the behavior of the function around those points. If the function changes from increasing to decreasing at a critical point, it corresponds to a relative maximum. Conversely, if the function changes from decreasing to increasing, it corresponds to a relative minimum.
Since we are only given the potential values for the critical points, we cannot directly determine which one corresponds to a relative maximum or minimum. We need more information about the behavior of the function around these points, such as the sign of the second derivative, to make a definitive conclusion.
Therefore, none of the given response options accurately identify the relative maximum and minimum of the polynomial function h(x).