Which of the following most accurately identifies the relative extrema of the polynomial function h(x)
?
(1 point)
Responses
There is a relative maximum at (0,−2)
and a relative minimum at (4,0)
.
There is a relative maximum at left parenthesis 0 comma negative 2 right parenthesis and a relative minimum at left parenthesis 4 comma 0 right parenthesis .
There is a relative minimum at (−2,0)
and a relative maximum at (0,4)
.
There is a relative minimum at left parenthesis negative 2 comma 0 right parenthesis and a relative maximum at left parenthesis 0 comma 4 right parenthesis .
There is a relative maximum at (−2,0)
and a relative minimum at (0,4)
.
There is a relative maximum at left parenthesis negative 2 comma 0 right parenthesis and a relative minimum at left parenthesis 0 comma 4 right parenthesis .
There is a relative minimum at (0,−2)
and a relative maximum at (4,0)
.
The correct response is: There is a relative maximum at (0,4) and a relative minimum at (4,0).
The correct response is:
There is a relative minimum at (−2,0) and a relative maximum at (0,4).
To determine the relative extrema of the polynomial function h(x), we need to find the critical points and analyze their values.
1. Find the derivative of the polynomial function h(x).
2. Set the derivative equal to zero to find the critical points.
3. Solve the equation to find the x-values of the critical points.
4. Plug the x-values into the original function h(x) to find the y-values of the critical points.
5. Analyze the values of the critical points to determine whether they are relative maximums or minimums.
Let's follow these steps:
1. Find the derivative of h(x) using the power rule or any other appropriate method.
2. Set the derivative equal to zero: h'(x) = 0.
3. Solve the equation h'(x) = 0 to find the x-values of the critical points.
4. Substitute the x-values into the original function h(x) to find the corresponding y-values.
5. Analyze the values of the critical points to determine whether they are relative maximums or minimums.
Following these steps will help us accurately identify the relative extrema of the polynomial function h(x).