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 $\left(x_{1}+x_{2}+x_{3}\right) / 3$.

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.

          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 $\left(x_{1}+x_{2}+x_{3}\right) / 3$.

Added by Mark S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

05/30/2023

Step 1

Step 1: Consider a general cubic function $ f(x) = ax^3 + bx^2 + cx + d $. Show more…

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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 $\left(x_{1}+x_{2}+x_{3}\right) / 3$.