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Chapter 3: Q. 14 (page 260)

Find the critical points of the function

f'(x)=(x-1)(x-2)x-3

Short Answer

Expert verified

Thecriticalpointsofthefunctionisx=1,2

Step by step solution

01

Step 1. Given 

The given function isf'(x)=(x-1)(x-2)x-3.

02

Step 2. Calculation 

"Apointx=cinthedomainoffiscalledacriticalpointoffiff'(c)=0orf'(c)doesnotexist.Now,equatef'(x)=0((x-1)(x-2))(x-3)=0(x-1)(x-2)=0x=1,x=2Therefore,thecriticalpointsofthefunctionisx=1,2

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Most popular questions from this chapter

For each set of sign charts in Exercises 53–62, sketch a possible

graph of f.

Determine whether or not each function fsatisfies the hypotheses of the Mean Value Theorem on the given interval [a,b]. For those that do, use derivatives and algebra to find the exact values of all c∈(a,b)that satisfy the conclusion of the Mean Value Theorem.

f(x)=tanx,[a,b]=[-π,π].

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.

fx=sexx

Find the possibility graph of its derivative f'.

Sketch careful, labeled graphs of each function f in Exercises 63–82 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.

f(x)=ln(x2+1)
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