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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

There exists a function f such that f(x) < 0, f′(x) < 0, and f″(x) > 0 for all x.

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.

Explanation

Results used:

Concavity test:

(a)If a function is such that f(x)>0 then the graph of f is concave upward.

(b) If a function is such that f(x)<0 then the graph of f is concave upward.

It is given that f(x)<0 thus graph of f is always below the x-axis

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