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Chapter 3: Q. 34 (page 261)

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.

f(x)=ln(lnx)

Short Answer

Expert verified

Ans: It has no solution hence this is a constant function.

Intervals of the given function are

Increasing at(1,鈭�)

Step by step solution

01

Step 1. Given information:

f(x)=ln(ln(x))

02

Step 2. Finding the derivative of the function:

f(x)=lnlnxf'(x)=1xlnxletf'(x)=0鈭�1xlnx=0鈬�10=xlnx鈬�xlnx=鈭�x=鈭�(nosolutions)

03

Step 3. Finding increasing and decreasing intervals: 

It has no solution hence this is a constant function.

so according to the graph, we can say that the function increases from 1

Therefore(1,鈭�)

04

Step 4. Verifying algebraic answers with graphs :

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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.

f(x)=1-xex

Prove that iff'' is zero on an interval, then f is linear on that interval.

Determine the graph of a function f from the graph of its derivative f'.

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.

f(x)=x2-1x2-5x+4

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.

f(x)=cos2(x)
See all solutions

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