Solution Found!
Show that if f '' > 0 throughout an interval [a, b], then
Chapter 4, Problem 19E(choose chapter or problem)
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?
Questions & Answers
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.