The function f(x)=2x^3−30x^2+54x+8 has one local minimum and one local maximum. Use a graph of the function to estimate these local extrema. This function has a local minimum at x = with output value: and a local maximum at x = with output value:

The function f(x)=2x^3−30x^2+54x+8 has one local minimum and one local maximum. Use a graph of the function to estimate these local extrema. This function has a local minimum at x = with output value: and a local maximum at x = with output 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^3−30x^2+54x+8 has one local minimum and one local maximum. Use a graph of the function to estimate these local extrema.

This function has a local minimum at x =

with output value:

and a local maximum at x =

with output 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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