Carmen was asked to identify the relative extrema of the polynomial function h(x) . Which of the following statements should she make?
Responses
There is an absolute minimum at x=0.5.
There is an absolute minimum at x is equal to 0 point 5. - not selected, this is the correct answer
There is an absolute minimum at x=0.5 and a relative minimum at x=2.
There is an absolute minimum at x is equal to 0 point 5 and a relative minimum at x is equal to 2. - incorrect
There is a relative maximum at x=0.5.
There is a relative maximum at x is equal to 0 point 5. - no response given
There is an absolute maximum at x=0.5.
explain how you get that answer
To identify the relative extrema of a polynomial function, Carmen needs to find the critical points by taking the derivative of the function, set it equal to zero, and solve for x.
In this case, if Carmen is looking for an absolute minimum, she needs to find the lowest point on the polynomial function. If the derivative of the function is positive to the left and negative to the right of a critical point, then that critical point represents an absolute minimum.
From the given options, Carmen should choose the statement "There is an absolute minimum at x=0.5."