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Chapter 4: Q. 1 TB (page 384)

Finding sign intervals: Consider the functionf(x)=x3鈭�4x2鈭�12x. Find the intervals on which f is positive and the intervals on which f is negative.

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Step by step solution

01

Step 1. GIven information:

f(x)=x3鈭�4x2鈭�12x

02

Step 2. Finding the roots of the function:

f(x)=x3鈭�4x2鈭�12xlet,f(x)=0x3鈭�4x2鈭�12x=0x3鈭�6x2+2x2鈭�12x=0x2x-6+2x(x-6)=0x-6(x2+2x)=0x-6(x(x+2))=0x(x-6)(x+2)=0so,rootsare0,-2,6

03

Step 3. Finding the positive and negative interval of the function:

a

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