   Chapter 3.6, Problem 12E

Chapter
Section
Textbook Problem

# 11–12 Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing graphs (with a graphing device) that display the major features of the curve. Use these graphs to estimate the maximum and minimum values. f ( x ) = ( 2 x + 3 ) 2 ( x − 2 ) 5 x 3 ( x − 5 ) 2

To determine

To sketch the graph of:

fx=2x+32x-25x3x-52

Explanation

1) Concept:

Find vertical and horizontal asymptotes of the given graph. Also, find intercepts, and by using the left hand and right hand limit towards the vertical asymptotes, check the behaviour of the graph and then plot the rough sketch of given function.

2) Given:

fx=2x+32x-25x3x-52

3) Calculation:

Asymptote:

Horizontal asymptotes:

limx-2x+32x-25x3x-52=- ,  limx+2x+32x-25x3x-52=

No Horizontal asymptote

Vertical asymptotes:

fx=2x+32x-25x3x-52

Vertical asymptote obtained at zeros of denominator,

That is,

x3x-52=0

x=0 or x-52=0

x=0 or x=0

Thus, vertical asymptote obtained when x=0, x=5

Intercepts:

For y intercept plug x=0  in the given function and solve it for y

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### let f(x) = x 1, g(x) = x+1, and h(x) = 2x3 1. Find the rule for each function. 10. g f

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Simplify: 948

Elementary Technical Mathematics

#### In problems 23-58, perform the indicated operations and simplify. 25.

Mathematical Applications for the Management, Life, and Social Sciences

#### The appropriate option for the value of (123).

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 