Brandon was asked to identify the relative maximum of the polynomial function h(x). Which answer choice identifies the correct value(s)?
(1 point)
Responses
There is a relative minimum at x=1.
There is a relative minimum at x equals 1 .
There is no relative maximum in this graph.
There is no relative maximum in this graph.
There is a relative maximum at x=0.
There is a relative maximum at x equals 0 .
There is a relative maximum at x=2.
There is a relative maximum at x=2.
To identify the relative maximum of the polynomial function h(x), we need to examine the behavior of the function near its critical points. Critical points occur where the derivative of the function is equal to zero or does not exist.
From the given answer choices, it seems that the correct value(s) of the relative maximum are either x=0 or x=2. However, without additional information or the equation of the function h(x), we cannot determine which value is correct.
To identify the relative maximum of a polynomial function, we need to examine the critical points of the function. Critical points occur where the derivative of the function is zero or undefined.
In this question, the answer choices provide the possible x-values for the critical points.
To find the relative maximum, we need to look for points where the derivative changes from positive to negative. This indicates a local peak or maximum.
Let's evaluate the given answer choices:
1. There is a relative minimum at x=1.
2. There is no relative maximum in this graph.
3. There is a relative maximum at x=0.
4. There is a relative maximum at x=2.
Based on the given answer choices, the correct answer would be option 3: "There is a relative maximum at x=0." This indicates that at x=0, the function has a relative maximum point.