f(x) = In (x² + 1) %3D Note: 2x and f"(x) = 2(1 – x)(1+ x) (x² + 1)² f'(x) %3D %3D x2 + 1 (a) Find domain (b) Find all intercepts

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...
icon
Related questions
icon
Concept explainers
Question
1. Let
f(x) = In (x2 + 1)
Note:
2x
and f"(x) =
2(1- x)(1+ x)
(x² + 1)²
f'(x) :
x2 + 1
(a) Find domain
(b) Find all intercepts
(c) Draw number line indicating where f is + or - or 0 or dne
(d) Draw number line indicating where f' is + or- or 0 or dne
(e) Find all local extremes and where they occur
(f) Draw number line indicating where f" is + or - or 0 or dne
(g) Find all inflection points
(h) Find all asymptotes
(i) Sketch a graph of f indicating local extremes and inflection points.
2. Sketch a graph of a function f that satisfies ALL number lines (one
raph, not three separate gr
tes)
Transcribed Image Text:1. Let f(x) = In (x2 + 1) Note: 2x and f"(x) = 2(1- x)(1+ x) (x² + 1)² f'(x) : x2 + 1 (a) Find domain (b) Find all intercepts (c) Draw number line indicating where f is + or - or 0 or dne (d) Draw number line indicating where f' is + or- or 0 or dne (e) Find all local extremes and where they occur (f) Draw number line indicating where f" is + or - or 0 or dne (g) Find all inflection points (h) Find all asymptotes (i) Sketch a graph of f indicating local extremes and inflection points. 2. Sketch a graph of a function f that satisfies ALL number lines (one raph, not three separate gr tes)
Expert Solution
Step 1

Here, we are going to solve the first two subparts and for the remaining subpart please post the question again.

Given,            f(x) =lnx2 + 1            f'(x) =2xx2 + 1            f"(x) =2(1-x)(1+x)x2+12

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Fundamentals of Algebraic Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning