Show that a cubic function (a third-degree polynomial) always has exactly one point of inflectio

Name: Show that a cubic function (a third-degree polynomial) always has exactly one point of inflection. If its graph has three x -intercepts x1, x2, and x3, show that the x -coordinate of the inflection point is (x1+x2+x3) / 3.
Uploaded: 2023-05-30T06:38:52-08:00
Duration: 1 min 32 s
Channel: Madhur L
Description: Show that a cubic function (a third-degree polynomial) always has exactly one point of inflection. If its graph has three x -intercepts x1, x2, and x3, show that the x -coordinate of the inflection point is (x1+x2+x3) / 3.

Question

Steven Clarke · Accepted Answer

1. A cubic function has the form $f(x) = ax^3 + bx^2 + cx + d$, where $a, b, c,$ and $d$ are con

Question

Show that a cubic function (a third-degree polynomial) always has exactly one point of inflection. If its graph has three $x$ -intercepts $x_{1}, x_{2},$ and $x_{3},$ show that the $x$ -coordinate of the inflection point is $\left(x_{1}+x_{2}+x_{3}\right) / 3.$

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