Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. f (x) = x3 - x2 - 2x - 1
A)relative maximum: (-0.55, -0.37)relative minimum: (1.22, -3.11)
B)relative maximum: (1.22, -3.11)relative minimum: (-0.55, -0.37)
C)relative maximum: (-0.37, -0.55)relative minimum: (-3.11, 1.22)
D)relative maximum: (-3.11, 1.22)relative minimum: (-0.37, -0.55)
E)relative maximum: (-3.11, -34.62)relative minimum: (-0.37, -0.45)

Question

Quizplus · Accepted Answer

The function $f(x) = x^3 - x^2 - 2x - 1$ is a cubic function, which typically has one relative maximum and one relative minimum. By graphing the function or using calculus to find the derivative and solve for critical points, we can determine the locations of these extrema. The correct coordinates for the relative maximum and minimum, as approximated to two decimal places, are given in option A: relative maximum at (-0.55, -0.37) and relative minimum at (1.22, -3.11). These points are found by identifying where the slope of the function (its derivative) equals zero and then determining whether these points are maxima or minima based on the concavity of the function or further derivative tests.

Use a Graphing Utility to Graph the Function and Approximate