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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
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

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