Solved: The sign-preserving property of continuous

Chapter 2, Problem 68E

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QUESTION:

PROBLEM 68E

The sign-preserving property of continuous functions Let ƒ be defined on an interval (a, b) and suppose that ƒ(c) ≠ 0 at some c where ƒ is continuous. Show that there is an interval about c where ƒ has the same sign as ƒ(c).

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QUESTION:

PROBLEM 68E

The sign-preserving property of continuous functions Let ƒ be defined on an interval (a, b) and suppose that ƒ(c) ≠ 0 at some c where ƒ is continuous. Show that there is an interval about c where ƒ has the same sign as ƒ(c).

ANSWER:

Solution :

Step 1 of 4 :

In this problem, we have to show that there is an interval  about c where ƒ has the same sign as ƒ(c).

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