What values of a and b make f(x)=x^3+ax^2+bx have Part 1 a. For a local maximum at x=−3 and a local minimum at x=7, a= ______ and b=_______. Part 2 b. For a local minimum at x=8 and a point of inflection at x=2, a= _______ and b= ______.

What values of a and b make f(x)=x^3+ax^2+bx have Part 1 a. For a local maximum at x=−3 and a local minimum at x=7, a= __ and b=_. Part 2 b. For a local minimum at x=8 and a point of inflection at x=2, a= _ and b= __.

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

What values of a and b make f(x)=x^3+ax^2+bx have

Part 1

For a local maximum at x=−3 and a local minimum at x=7, a= ______ and b=_______.

Part 2

b. For a local minimum at x=8 and a point of inflection at x=2, a= _______ and b= ______.

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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