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 9RQ
To determine

Whether the statement, there exist a function f such that f(x)>0,f(x)<0 and f(x)>0 for all x  is true or false.

Expert Solution

Answer to Problem 9RQ

The given statement is true.

Explanation of Solution

Consider a function in such a way that f(x)>0 . So, consider f(x)=1x .

Differentiate f with respect to x.

f(x)=1x2

Thus, f(x)<0 for all x.

Find the second derivative of f(x) .

f(x)=2xx4=2x3

The second derivative function, f(x)>0 for all x.

Therefore, the given statement is true.

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