Answered: The function f(x)=4+3x+12x^−1 has one…

The function f(x)=4+3x+12x^−1 has one local minimum and one local maximum. This function has a local maximum at x= with value= and a local minimum 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)=4+3x+12x^−1 has one local minimum and one local maximum.
This function has a local maximum at x=
with value=

and a local minimum at x=
with value=

Formula Formula A function f ( x ) is also said to have attained a local minimum 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 a case f ( a ) is called the local minimum value of f ( x ) at x = a .

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