Which of the following most accurately identifies the relative maximum and minimum of the polynomial function h(x) ?
Responses
There is a relative maximum at x=1.5 and a relative minimum at x=−2.
There is a relative maximum at x is equal to 1 point 5 and a relative minimum at x is equal to negative 2. - no response given
There is a relative minimum at x=−1 and a relative maximum at x=0.555.
There is a relative minimum at x is equal to negative 1 and a relative maximum at x is equal to 0 point 5 5 5. - incorrect
There is a relative maximum at x=−1 and a relative minimum at x=0.555.
There is a relative maximum at x is equal to negative 1 and a relative minimum at x is equal to 0 point 5 5 5. - not selected, this is the correct answer
There is a relative maximum at x=−1 and no relative minimum.
explain how you get the answer
To determine the relative maximum and minimum of a polynomial function, we look for the points where the first derivative equals zero.
In this case, the correct answer is "There is a relative maximum at x=−1 and a relative minimum at x=0.555."
To find this, take the derivative of h(x) and set it equal to zero:
h'(x) = 0
Then solve for x. The solution x = -1 represents the relative maximum, while x = 0.555 represents the relative minimum.