Question

Use polynomial graph shape and end behavior to determine which of the following could be the x-coordinates at which

the relative maximum and relative minimum occur in the given function.
f(x)- 8x³-4x²+6
a. The relative maximum is at x - 1 and the relative minimum is at x = 0.33.
b. The relative maximum is at x - 1 and the relative minimum is at x = -0.33.
c. The relative maximum is at x = 0 and the relative minimum is at x = 0.33.
d. The relative maximum is at x = 0 and the relative minimum is at x = -0.33.

Answer 1

To determine the x-coordinates of the relative maximum and minimum in a polynomial function, analyze the graph's shape and end behavior.

Step-by-step explanation:

To determine the x-coordinates at which the relative maximum and relative minimum occur in a polynomial function, we can look at the shape of the graph and the end behavior. For the given function f(x) = 8x³ - 4x² + 6, the leading term is positive (8x³), indicating that the graph opens upward. This means that there will be a relative minimum at x = 0, where the graph transitions from decreasing to increasing. The graph will continue to increase indefinitely as x approaches negative infinity and positive infinity, so there is no relative maximum. Therefore, the correct option is c. The relative maximum is at x = 0 and the relative minimum is at x = 0.33.

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