Show that if f '' > 0 throughout an interval [a, b], then

Chapter 4, Problem 19E

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QUESTION:

Problem 19E

Show that if f '' > 0 throughout an interval [a, b], then f ' has at most one zero in [a, b]. What if f '' < 0 throughout [a, b] instead?

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QUESTION:

Problem 19E

Show that if f '' > 0 throughout an interval [a, b], then f ' has at most one zero in [a, b]. What if f '' < 0 throughout [a, b] instead?

ANSWER:

Solution

Step 1 of 4

In this problem we have to show that if f '' > 0 or  throughout an interval [a, b], then f ' has at most one zero in [a, b].

First consider the case f '' > 0 .

Given that exists throughout

Therefore the derivative function is continuous in this interval.


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