Perform a first derivative test on the function f(x)=2x3 +3x2 −12x +4;[−2,4]. a. b.Use the first derivative test to locate the local maximum and minimum values. c. Identify the absolute minimum and maximum values of the function on the given interval (when they exist).

Perform a first derivative test on the function f(x)=2x3 +3x2 −12x +4;[−2,4]. a. b.Use the first derivative test to locate the local maximum and minimum values. c. Identify the absolute minimum and maximum values of the function on the given interval (when they exist).

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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Question

Perform a first derivative test on the function

f(x)=2x³ +3x² −12x +4;[−2,4].

b.Use the first derivative test to locate the local maximum and minimum values.
c. Identify the absolute minimum and maximum values of the function on the given interval (when they exist).

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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