Answered: The function f(x)=−2x^3+21x^2−36x+7 has…

The function f(x)=−2x^3+21x^2−36x+7 has one local minimum and one local maximum. This function has a local minimum at x = with value= and a local maximum at x = with value=

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 3SE: How are the absolute maximum and minimum similar to and different from the local extrema?

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Question

The function f(x)=−2x^3+21x^2−36x+7 has one local minimum and one local maximum.
This function has a local minimum at x =
with value=

and a local maximum at x =
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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