For the graph of the function g(x) = x³-x²-4x+4, g(1.535) = -0.879 is the minimum point and g(-0.869) = 6.065 is the maximum point. g(1/3) = 2.593 is the inflection point.
The graph of a function f is the set of all points in the plane of the form (x, f(x)).
To graph the function ⇒ substitute with the values of x and get g(x) but at first we need to find the critical points (maximum, minimum, inflection) which can be found by differentiating g(x) with respect to x.
Inflection points are points where the function changes concavity, i.e. from being "concave up" to being "concave down" or vice versa.
Points in the domain of definition of a real-valued function at which it takes its greatest and smallest values; such points are also called absolute maximum and absolute minimum points.
g'(x) = 3x² -2x-4 = 0
⇒ x = 1.535 and -0.869
⇒ maximum and minimum points
g(1.535) = -0.879 which is the minimum point
g(-0.869) = 6.065 which is the maximum point
g"(x) = 6x -2 = 0
⇒ x = 1/3
⇒ point of Inflection: g(1/3) = 2.593
To learn more about point of Inflection: https://brainly.com/question/5928704
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