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The function f (x, y) = 3x3+y2-9x+4y is given. a) Find the critical points of function f. b)Do these functions have the local maximum, local minimum and saddle points at these points? Determine

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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The function f (x, y) = 3x³+y²-9x+4y is given.

a) Find the critical points of function f.

b)Do these functions have the local maximum, local minimum and saddle points at these points? Determine.

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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