1. Sketch the graph of f(x) = x3 - x4 + 6x2 + 3 by applying differentiation methods for analyzing where the graph is increasing/decreasing, local maximum/minimum points [Using the second derivative test], concave up/down intervals with inflection points. 1. Sketch the graph of f(x) = x³ - x4 + 6x² + 3 by applying differentiation methods foranalyzing where the graph is increasing/decreasing, local maximum/minimum points[Using the second derivative test], concave up/down intervals with inflection points.(Ctrl)▼

The given function is .The aim is to find the increasing and decreasing intervals, local maximum and…

Sketch the graph of f(x) = x³ - x4 + 6x² + 3 by applying differentiation methods for analyzing where the graph is increasing/decreasing, local maximum/minimum points [Using the second derivative test], concave up/down intervals with inflection points.

Sketch the graph of f(x) = x³ - x4 + 6x² + 3 by applying differentiation methods for analyzing where the graph is increasing/decreasing, local maximum/minimum points [Using the second derivative test], concave up/down intervals with inflection points.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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Question

1. Sketch the graph of f(x) = x³ - x⁴ + 6x² + 3 by applying differentiation methods for analyzing where the graph is increasing/decreasing, local maximum/minimum points [Using the second derivative test], concave up/down intervals with inflection points.

1. Sketch the graph of f(x) = x³ - x4 + 6x² + 3 by applying differentiation methods for
analyzing where the graph is increasing/decreasing, local maximum/minimum points
[Using the second derivative test], concave up/down intervals with inflection points.
(Ctrl)
▼

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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Step 1: Determine the given information:

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Step 2: Find the critical points

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Step 3: Find increasing and decreasing intervals

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Step 4: Local maximum and local minimum points

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Step 5: Concavity intervals

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Step 6: Graph of the function

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