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Chapter 3: Q. 10 (page 314)

Find all roots, local maxima and minima, and inflection points of each function f . In addition, determine whether any local extrema are also global extrema on the domain of f .

f(x)=x3鈭�15x2鈭�33x

Short Answer

Expert verified

x=0,16.95,-1.95

Step by step solution

01

Step 1. Given Information

Consider a function

f(x)=x3鈭�15x2鈭�33x

02

Step 2. Calculation for roots

For finding roots of the function;

f(x)=0x3鈭�15x2鈭�33x=0xx2鈭�15x鈭�33=0Eitherx=0orx2鈭�15x鈭�33=0x=0orx=15卤(鈭�15)2鈭�4鈰�1鈰�(鈭�33)2鈰�1x=0orx=15卤255+1322x=0orx=15卤3572x=0,16.95,鈭�1.95

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Most popular questions from this chapter

Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

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Use a sign chart for f'to determine the intervals on which each function fis increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

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Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

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Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

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Sketch careful, labeled graphs of each function f in Exercises 63鈥�82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of f,f',andf'', and examine any relevant limits so that you can describe all key points and behaviors of f.

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