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Chapter 2: Q. 9 (page 89)

Concepts and Vocabulary

True or False: A function f has a local maximum at c if there is an open interval I containing c so that for all x in I, f(x)≤f(c)

Short Answer

Expert verified

True

Step by step solution

01

Given Information 

A function f has a local maximum at c if there is an open interval I containing c so that for all x in I, f(x)≤f(c)

02

local maximum or minimum 

If the value of f at c is less than or equal to the values of f on I, then f has a local

minimum at c.

If the value of f at c is greater than or equal to the values of f on I, then f has a local

maximum at c.

A function f has a local maximum at c if there is an open interval I containing c so that for all x in I, f(x)≤f(c). We call f(c) a local maximum value of f. Given statement is true.

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Most popular questions from this chapter

True or False The domain of the function f(x)=x2-4xis{x|x≠±2}.

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

True or False

The graph of y=-f(x)is the reflection about the x-axis of the graph of y=f(x).

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

f(x)=x2+4

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.

g(x)=x2+3x2-1
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