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Chapter 1: Q. 16 (page 120)

Sketch a labeled graph of a function that satisfies the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem follows.

Short Answer

Expert verified

A labeled graph of a function that satisfies the hypothesis of the Extreme Value Theorem is

Step by step solution

01

Step 1. Given Information.

The Extreme Value Theorem states that if f is continuous on a closed interval[a, b], then there exist values M and m in the interval [a, b]such that f(M) is the maximum value of f(x) on [a, b] and f(m) is the minimum value of f(x) on [a, b].

02

Step 2. Sketching a graph

The graph is

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Most popular questions from this chapter

For each limit statement , use algebra to find δ > 0 in terms of ε> 0 so that if 0 < |x − c| < δ, then | f(x) − L| < ε.

limx→0(x3+1)=1

For each limit statement , use algebra to find δ > 0 in terms of ε> 0 so that if 0 < |x − c| < δ, then | f(x) − L| < ε.

limx→2(x2-4x+6)=2

Sketch a labeled graph of a function that satisfies the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem follows.

Write delta-epsilon proofs for each of the limit statements in Exercises 47–60.

limx→2x2-3x+2x-2=1

limx→π1cosec(π-x)
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