The function f(x)=2x^3−42x^2+270x+1 has one local minimum and one local maximum. This function has a local minimum at x equals ______, with value_______ and a local maximum at x equals _______, with value ________

The function f(x)=2x^3−42x^2+270x+1 has one local minimum and one local maximum. This function has a local minimum at x equals __, with value_ and a local maximum at x equals _, with value ____

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

Problem 35E: Formula for Maximum and Minimum Values Find the maximum or minimum value of the function....

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Question

The function f(x)=2x^3−42x^2+270x+1 has one local minimum and one local maximum.
This function has a local minimum at x equals ______, with value_______

and a local maximum at x equals _______, with value ________

Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .

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