For the function f (x) = x4 - 4x3 + 5, find the local and absolute extrema and any points of inflection in the interval [-1,4]. Write all answers as points. If there are none, write "none" and show why. Show ALL work.

For the function f (x) = x4 - 4x3 + 5, find the local and absolute extrema and any points of inflection in the interval [-1,4]. Write all answers as points. If there are none, write "none" and show why. Show ALL work.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Show all work

Local extrema (maxima and minima)

Absolute extrema (abs max and abs min)

inflection point(s)

For the function f (x) = x4 – 4x3 + 5, find the local and absolute
extrema and any points of inflection in the interval [-1,4]. Write
all answers as points. If there are none, write "none" and show
why. Show ALL work.
-

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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