Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 − 8x2 + 4 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value

Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 − 8x2 + 4 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.1: Quadratic Functions

Problem 77E: Minimizing cost A company that produces and sells digital cameras has determined that the total...

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Question

Consider the equation below. (If an answer does not exist, enter DNE.)

f(x) = x⁴ − 8x² + 4

(a) Find the interval on which f is increasing. (Enter your answer using interval notation.)

Find the interval on which f is decreasing. (Enter your answer using interval notation.)

(b) Find the local minimum and maximum values of f.

local minimum value
local maximum value

(x, y) =

(smaller x-value)

(x, y) =

(larger x-value)

Find the interval on which f is concave up. (Enter your answer using interval notation.)

Find the interval on which f is concave down.(Enter your answer using interval notation.)

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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