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Chapter 3: Q. 0 (page 286)

Q.Read the section and make your own summary of the material.

Short Answer

Expert verified

To find a global extremum of a continuous function we must compare the following:

  • the valuesf(c) for each interior local extremum c ∈ I
  • the values f(c) at any closed endpoints x = cof I
  • the limits limx→cf(x) at any open endpoints or non-domain points x = cof I.

Many students have difficulty with word problems because of the translation step, not because of the mathematical solving step. This translating procedure is illustrated in the following diagram:

Step by step solution

01

Step 1. Given Information.

The information in the book.

02

Step 2. Finding Global extrema.

To find a global extremum of a continuous function we must compare the following:

  • the valuesf(c) for each interior local extremum c ∈ I
  • the values f(c) at any closed endpoints x = cof I
  • the limits limx→cf(x) at any open endpoints or non-domain points x = cof I.
03

Step 3. Translating Word Problems into Mathematical Problems.

Many students have difficulty with word problems because of the translation step, not because of the mathematical solving step. This translating procedure is illustrated in the following diagram:

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Most popular questions from this chapter

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

Use the second-derivative test to determine the local extrema of each function fin Exercises 29-40. If the second-derivative test fails, you may use the first-derivative test. Then verify your algebraic answers with graphs from a calculator or graphing utility. (Note: These are the same functions that you examined with the first-derivative test in Exercises 39-50of Section 3.2.)

f(x)=(x-2)2(1+x)

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)=2x3−9x2+1

It took Alina half an hour to drive to the grocery store that is 20 miles from her house.

(a) Use the Mean Value Theorem to show that, at some point during her trip, Alina must have been traveling exactly 40 miles per hour.

(b) Why does what you have shown in part (a) make sense in real-world terms?

Find the possibility graph of its derivative f'.
See all solutions

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