Let f(x) = (2x+1)/(x+1)2. (d) Determine the horizontal asymptote(s) of the curve y=f(x) (if any). (e) Find the intervals of increase/decrease of f, given that f'(x)=(-2x)/(x+1)3. (f) Determine the points at which f has a local maximum/minimum (if any

Let f(x) = (2x+1)/(x+1)2. (d) Determine the horizontal asymptote(s) of the curve y=f(x) (if any). (e) Find the intervals of increase/decrease of f, given that f'(x)=(-2x)/(x+1)3. (f) Determine the points at which f has a local maximum/minimum (if any

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

Let f(x) = (2x+1)/(x+1)².

(d) Determine the horizontal asymptote(s) of the curve y=f(x) (if any).

(e) Find the intervals of increase/decrease of f, given that f'(x)=(-2x)/(x+1)³.

(f) Determine the points at which f has a local maximum/minimum (if any).

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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