Given the equation of the function y=x3– 12x2+ 36x – 11. find the following: • the expression for y • the critical points of the function; • the expression for y" • the point of inflection of the function; • the slope of the inflectional tangent of y=f(x): • the equation of the inflectional tangent of y=f (x); • Is the function increasing or decreasing at the point of inflection? Briefly explain your answer. Note: The inflectional tangent is the tangent line of f(x) at the point of inflection.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.1: Quadratic Functions And Models
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Given the equation of the function y=x3– 12x2+ 36x – 11 find the following:
• the expression for y
the critical points of the function;
• the expression for y"
• the point of inflection of the function;
• the slope of the inflectional tangent of y =f (x):
the equation of the inflectional tangent of y=f(x);
• Is the function increasing or decreasing at the point of inflection? Briefly explain your answer.
Note: The inflectional tangent is the tangent line of f(x) at the point of inflection.
Transcribed Image Text:Given the equation of the function y=x3– 12x2+ 36x – 11 find the following: • the expression for y the critical points of the function; • the expression for y" • the point of inflection of the function; • the slope of the inflectional tangent of y =f (x): the equation of the inflectional tangent of y=f(x); • Is the function increasing or decreasing at the point of inflection? Briefly explain your answer. Note: The inflectional tangent is the tangent line of f(x) at the point of inflection.
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