BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 4, Problem 19RQ
To determine

Whether the statement, if f(x) exists and non zero for all values of x then f(1)f(0) is true or false.

Expert Solution

Answer to Problem 19RQ

The given statement is true.

Explanation of Solution

As f(x)0 there exist two cases.

Case 1:

Let f(x)>0 for all values of x .

Then the function f is strictly increasing function.

Therefore, f(1)f(0) .

Case 2:

Let f(x)<0 for all values of x .

Then the function f is strictly decreasing function.

So, f(1)f(0) .

Therefore, in both the cases f(1)f(0)

Hence the given statement is true.

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