Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x5 ln(x) (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)

Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x5 ln(x) (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)

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

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Question

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

f(x) = x⁵ ln(x)

(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

(c)

Find the inflection point.

(x, y) = ( )

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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